diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml
index bf4b68a7a..a17a8eb7a 100644
--- a/.github/workflows/docs.yml
+++ b/.github/workflows/docs.yml
@@ -14,12 +14,16 @@ concurrency:
 
 jobs:
   build:
-    runs-on: ubuntu-latest
+    runs-on: ubuntu-24.04
+    env:
+      CARGO_BUILD_JOBS: '2'
+      CMAKE_BUILD_PARALLEL_LEVEL: '2'
+      RUST_TEST_THREADS: '2'
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262 # v4
 
       - name: Read Open Question Board source
-        uses: actions/checkout@v4
+        uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262 # v4
         with:
           repository: GiggleLiu/autoresearch-gadgets
           ref: main
@@ -32,11 +36,17 @@ jobs:
       - name: Build Open Question Board
         run: uv run --project open-questions-source/website --locked python open-questions-source/website/build.py
 
-      - uses: dtolnay/rust-toolchain@stable
+      - uses: dtolnay/rust-toolchain@b725eda525362e7cf34af9a7243cac1e3f01a7ec # stable
+        with:
+          toolchain: '1.99.0'
+          targets: wasm32-unknown-unknown
+
+      - name: Install browser binding tools
+        run: cargo install wasm-bindgen-cli --version 0.2.129 --locked
 
-      - uses: actions/setup-node@v4
+      - uses: actions/setup-node@49933ea5288caeca8642d1e84afbd3f7d6820020 # v4
         with:
-          node-version: '22'
+          node-version: '24.21.0'
           cache: npm
 
       - name: Install mdBook
@@ -54,50 +64,24 @@ jobs:
           tar -xJf typst.tar.xz
           mv typst-x86_64-unknown-linux-musl/typst "$HOME/bin/"
 
-      - name: Install Node dependencies
-        run: npm ci
-
-      - name: Generate data
+      - name: Build and verify deployment artifact
         run: |
-          cargo run --features "example-db" --example export_examples
-          cargo run --example export_petersen_mapping
-          cargo run --example export_graph
-          node scripts/generate_reduction_graph_layout.js
-          cargo run --example export_schemas
-          cargo build -p problemreductions-cli --bin pred
-          bash scripts/generate_doc_snippets.sh target/debug/pred
-
-      - name: Build mdBook
-        run: mdbook build
-
-      - name: Build PDF
-        run: typst compile --root . docs/paper/reductions.typ book/reductions.pdf
-
-      - name: Build rustdoc
-        run: RUSTDOCFLAGS="--default-theme=dark" cargo doc --no-deps
-
-      - name: Combine documentation
-        run: |
-          mkdir -p book/api
-          cp -r target/doc/* book/api/
-
-      - name: Build research website
-        run: python3 scripts/build_website.py --open-questions open-questions-source/website/dist
-
-      - name: Verify deployment artifact
-        run: |
-          python3 -m pip install playwright==1.58.0
-          python3 -m playwright install --with-deps chromium
+          uv run --python 3.12.14 --no-project --with-requirements scripts/website-requirements.txt python -m playwright install --with-deps chromium firefox webkit
+          uv run --python 3.12.14 --no-project --with-requirements scripts/website-requirements.txt python scripts/check_website.py --output book --open-questions open-questions-source/website/dist
           npm audit --audit-level=moderate
-          npm run test:reduction-graph-js
-          python3 -m unittest discover -s scripts -p 'test_website_build.py'
-          python3 -m http.server 3001 --bind 127.0.0.1 --directory book &
-          server_pid=$!
-          trap 'kill "$server_pid"' EXIT
-          python3 scripts/test_website.py
+          git diff --exit-code -- Cargo.lock package-lock.json
+
+      - name: Retain verification diagnostics
+        if: always()
+        uses: actions/upload-artifact@ea165f8d65b6e75b540449e92b4886f43607fa02 # v4
+        with:
+          name: website-verification
+          path: |
+            book/verification.json
+            book/verification.log
 
       - name: Upload artifact
-        uses: actions/upload-pages-artifact@v3
+        uses: actions/upload-pages-artifact@56afc609e74202658d3ffba0e8f6dda462b719fa # v3
         with:
           path: './book'
 
@@ -109,11 +93,11 @@ jobs:
     environment:
       name: github-pages
       url: ${{ steps.deployment.outputs.page_url }}
-    runs-on: ubuntu-latest
+    runs-on: ubuntu-24.04
     needs: build
     steps:
       - name: Setup Pages
-        uses: actions/configure-pages@v4
+        uses: actions/configure-pages@1f0c5cde4bc74cd7e1254d0cb4de8d49e9068c7d # v4
       - name: Deploy to GitHub Pages
         id: deployment
-        uses: actions/deploy-pages@v4
+        uses: actions/deploy-pages@d6db90164ac5ed86f2b6aed7e0febac5b3c0c03e # v4
diff --git a/.gitignore b/.gitignore
index fc59be7ea..756c20c27 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,6 +1,5 @@
 # Rust
 /target/
-Cargo.lock
 **/*.rs.bk
 *.pdb
 
@@ -74,6 +73,8 @@ tarpaulin-report.html
 
 # Generated documents
 *.pdf
+docs/website/baselines/
+/docs/website/*preview.png
 
 # Reference packages (downloaded for comparison)
 pkgref/
@@ -90,6 +91,12 @@ claude-output.log
 *.json
 !package.json
 !package-lock.json
+!tsconfig.json
+!docs/website/graph-scene.schema.json
+!docs/website/graph-details.schema.json
+!docs/website/path-graph.schema.json
+!docs/website/atlas-data.schema.json
+!docs/website/native-exports.schema.json
 .claude/worktrees/
 docs/test-reports/
 docs/superpowers/
@@ -99,3 +106,5 @@ docs/src/generated/
 .claude/projects/
 docs/research/
 docs/solutions/
+
+/docs/website/src/generated/
diff --git a/Cargo.lock b/Cargo.lock
new file mode 100644
index 000000000..b700b8b5f
--- /dev/null
+++ b/Cargo.lock
@@ -0,0 +1,1870 @@
+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
+version = 4
+
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+[[package]]
+name = "wasip2"
+version = "1.0.4+wasi-0.2.12"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b67efb37e106e55ce722a510d6b5f9c17f083e5fc79afc2badeb12cc313d9487"
+dependencies = [
+ "wit-bindgen",
+]
+
+[[package]]
+name = "wasm-bindgen"
+version = "0.2.129"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "9bb54f33acc68fd454578d9820b0bde1a1a3d17aa17bb7b6595806d02886d409"
+dependencies = [
+ "cfg-if",
+ "once_cell",
+ "rustversion",
+ "wasm-bindgen-macro",
+ "wasm-bindgen-shared",
+]
+
+[[package]]
+name = "wasm-bindgen-macro"
+version = "0.2.129"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "2e29d0c35b16e224a7eeb5cd2d25e3e1968fbd65604117b44d3b789d00ee8535"
+dependencies = [
+ "quote",
+ "wasm-bindgen-macro-support",
+]
+
+[[package]]
+name = "wasm-bindgen-macro-support"
+version = "0.2.129"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "6f501a8bc3719dba86ef8ae4728879c08001bea749eb1333ac5b91e040e2a6b7"
+dependencies = [
+ "bumpalo",
+ "proc-macro2",
+ "quote",
+ "syn 3.0.7",
+ "wasm-bindgen-shared",
+]
+
+[[package]]
+name = "wasm-bindgen-shared"
+version = "0.2.129"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "23f0c9c52aa7cd7d77769a4cfe2a9adb1b331f489a41d912ce14513d5ab995c6"
+dependencies = [
+ "unicode-ident",
+]
+
+[[package]]
+name = "web-sys"
+version = "0.3.106"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "88261b9deccee56594c11a3460c462c41f58d148598fe70ad77070126a68aba4"
+dependencies = [
+ "js-sys",
+ "wasm-bindgen",
+]
+
+[[package]]
+name = "winapi"
+version = "0.3.9"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "5c839a674fcd7a98952e593242ea400abe93992746761e38641405d28b00f419"
+dependencies = [
+ "winapi-i686-pc-windows-gnu",
+ "winapi-x86_64-pc-windows-gnu",
+]
+
+[[package]]
+name = "winapi-i686-pc-windows-gnu"
+version = "0.4.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "ac3b87c63620426dd9b991e5ce0329eff545bccbbb34f3be09ff6fb6ab51b7b6"
+
+[[package]]
+name = "winapi-util"
+version = "0.1.11"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "c2a7b1c03c876122aa43f3020e6c3c3ee5c05081c9a00739faf7503aeba10d22"
+dependencies = [
+ "windows-sys",
+]
+
+[[package]]
+name = "winapi-x86_64-pc-windows-gnu"
+version = "0.4.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "712e227841d057c1ee1cd2fb22fa7e5a5461ae8e48fa2ca79ec42cfc1931183f"
+
+[[package]]
+name = "windows-core"
+version = "0.62.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b8e83a14d34d0623b51dce9581199302a221863196a1dde71a7663a4c2be9deb"
+dependencies = [
+ "windows-implement",
+ "windows-interface",
+ "windows-link",
+ "windows-result",
+ "windows-strings",
+]
+
+[[package]]
+name = "windows-implement"
+version = "0.60.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "053e2e040ab57b9dc951b72c264860db7eb3b0200ba345b4e4c3b14f67855ddf"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn 2.0.119",
+]
+
+[[package]]
+name = "windows-interface"
+version = "0.59.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "3f316c4a2570ba26bbec722032c4099d8c8bc095efccdc15688708623367e358"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn 2.0.119",
+]
+
+[[package]]
+name = "windows-link"
+version = "0.2.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f0805222e57f7521d6a62e36fa9163bc891acd422f971defe97d64e70d0a4fe5"
+
+[[package]]
+name = "windows-result"
+version = "0.4.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7781fa89eaf60850ac3d2da7af8e5242a5ea78d1a11c49bf2910bb5a73853eb5"
+dependencies = [
+ "windows-link",
+]
+
+[[package]]
+name = "windows-strings"
+version = "0.5.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7837d08f69c77cf6b07689544538e017c1bfcf57e34b4c0ff58e6c2cd3b37091"
+dependencies = [
+ "windows-link",
+]
+
+[[package]]
+name = "windows-sys"
+version = "0.61.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "ae137229bcbd6cdf0f7b80a31df61766145077ddf49416a728b02cb3921ff3fc"
+dependencies = [
+ "windows-link",
+]
+
+[[package]]
+name = "wit-bindgen"
+version = "0.57.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1ebf944e87a7c253233ad6766e082e3cd714b5d03812acc24c318f549614536e"
+
+[[package]]
+name = "zerocopy"
+version = "0.8.62"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "86502bf56ac7c77571a32e2647bb2a15894565e981fb2a48d7bde2d91c965a9d"
+dependencies = [
+ "zerocopy-derive",
+]
+
+[[package]]
+name = "zerocopy-derive"
+version = "0.8.62"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "5457206954b06561e2608c7e19cf58b1926586d999c246eebe4502f7e2039d1a"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn 2.0.119",
+]
+
+[[package]]
+name = "zmij"
+version = "1.0.23"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "29666d0abbfad1e3dc4dcf6144730dd3a3ab225bbbdac83319345b1b44ccfc1b"
diff --git a/Cargo.toml b/Cargo.toml
index 3117e15e7..8ec0452c3 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -4,6 +4,7 @@ members = [
     "problemreductions-expr",
     "problemreductions-macros",
     "problemreductions-cli",
+    "problemreductions-web",
 ]
 
 [package]
@@ -22,7 +23,6 @@ benchmarks = ["dep:criterion"]
 
 [dependencies]
 petgraph = { version = "0.8.3", features = ["serde-1"] }
-bitvec = "1.1.1"
 serde = { version = "1.0.229", features = ["derive"] }
 # Persisted problem and reduction data must preserve every finite f64 on replay.
 serde_json = { version = "1.0.151", features = ["float_roundtrip"] }
@@ -61,3 +61,9 @@ debug = "full"
 lto = true
 codegen-units = 1
 strip = true
+
+# Size-optimized build for the browser (scripts/build_website.py).
+[profile.wasm-release]
+inherits = "release"
+opt-level = "z"
+panic = "abort"
diff --git a/Makefile b/Makefile
index 6b0a5db5c..d55937539 100644
--- a/Makefile
+++ b/Makefile
@@ -1,6 +1,6 @@
 # Makefile for problemreductions
 
-.PHONY: help build test bench mcp-test fmt clippy doc mdbook website paper paper-data clean coverage rust-export compare qubo-testdata export-schemas release diagrams jl-testdata cli cli-demo copilot-review papers papers-lookup papers-download papers-scihub papers-status papers-push papers-pull papers-index
+.PHONY: help build test bench mcp-test fmt clippy doc mdbook website website-data paper paper-data clean coverage rust-export compare qubo-testdata export-schemas release diagrams jl-testdata cli cli-demo copilot-review papers papers-lookup papers-download papers-scihub papers-status papers-push papers-pull papers-index
 
 TEST_FEATURES := example-db
 
@@ -77,13 +77,16 @@ paper-data:
 	cargo run --features "$(TEST_FEATURES)" --example export_examples
 	cargo run --features "$(TEST_FEATURES)" --example export_petersen_mapping
 
-# Build mdBook documentation
-doc: node_modules/elkjs/package.json paper-data
+# Fresh shared inputs for mdBook, the website, and isolated verification builds.
+website-data: node_modules/elkjs/package.json paper-data
 	cargo run --example export_graph
 	node scripts/generate_reduction_graph_layout.js
 	cargo run --example export_schemas
 	cargo build -p problemreductions-cli --bin pred
 	bash scripts/generate_doc_snippets.sh target/debug/pred
+
+# Build mdBook documentation
+doc: website-data
 	mdbook build
 	RUSTDOCFLAGS="--default-theme=dark" cargo doc --no-deps
 	rm -rf book/api
@@ -91,18 +94,12 @@ doc: node_modules/elkjs/package.json paper-data
 	python3 scripts/build_website.py
 
 # Build the product website with fresh atlas data; API/PDF builds remain in doc/paper.
-website: node_modules/elkjs/package.json paper-data
-	cargo run --example export_graph
-	node scripts/generate_reduction_graph_layout.js
-	cargo run --example export_schemas
-	cargo build -p problemreductions-cli --bin pred
-	bash scripts/generate_doc_snippets.sh target/debug/pred
+website: website-data
 	mdbook build
 	python3 scripts/build_website.py
 
 # Generate SVG diagrams from Typst sources (light + dark themes)
 TYPST_DOC_DIAGRAMS := $(wildcard docs/src/static/*.typ)
-TYPST_PAPER_DIAGRAMS := $(wildcard docs/paper/static/*.typ)
 diagrams:
 	@for src in $(TYPST_DOC_DIAGRAMS); do \
 		base=$$(basename $$src .typ); \
@@ -229,7 +226,6 @@ compare: rust-export
 	done
 
 # Closed-loop CLI demo: exercises all commands end-to-end
-PRED := cargo run -p problemreductions-cli --release --
 CLI_DEMO_DIR := /tmp/pred-cli-demo
 cli-demo: cli
 	@echo "=== pred CLI closed-loop demo ==="
diff --git a/docs/src/design.md b/docs/src/design.md
index a8710a5a6..50f42e66e 100644
--- a/docs/src/design.md
+++ b/docs/src/design.md
@@ -541,12 +541,16 @@ Output: ProblemParameters { num_vars: 25 }
 ```
 
 For multi-step paths, `compose_path_parameter_transform` substitutes each step into the next.
-When only upper bounds are known for the intermediate fields, a downstream polynomial is
-first fully expanded and like monomials are combined; terms with non-positive coefficients
-are then removed before substitution. For example, `m <= n^2` followed by `k = 10 - m`
-produces the sound bound `k <= 10`, while
-`e' = v(v - 1)/2 - e` produces `e' <= v^2/2`. A non-polynomial downstream formula cannot
-propagate symbolic upper bounds and makes that field unavailable, preserving the other fields. Projection to `Growth` is a separate descriptive terminal operation used for
+The shared `ParameterTransform::compose` engine first expands downstream polynomials
+and combines like monomials, so cancelled dependencies disappear. Its partial hull
+removes a negative monomial only if it involves an upper-bounded intermediate field;
+negative terms involving exclusively exact inputs are retained. For example,
+`v = n`, `e <= n^2` followed by `e' = v(v - 1)/2 - e` produces
+`e' <= n(n - 1)/2`, keeping the exact `-n/2` term. With `v <= n` instead,
+that term is also dropped and the certificate is `e' <= n^2/2`.
+Likewise, `m <= n^2` followed by `k = 10 - m` produces `k <= 10`.
+A non-polynomial downstream formula cannot propagate symbolic upper bounds and
+makes that field unavailable, preserving the other fields. Projection to `Growth` is a separate descriptive terminal operation used for
 Big-O display; it does not rank or filter paths.
 
 </details>
diff --git a/docs/src/introduction.md b/docs/src/introduction.md
index 49570e0a3..ff990fd09 100644
--- a/docs/src/introduction.md
+++ b/docs/src/introduction.md
@@ -4,9 +4,12 @@ Problem Reductions is a Rust library and command-line tool for NP-hard problems
 
 {{#include generated/catalog-counts.md}}
 
-- [Atlas](index.html#atlas): every problem variant and reduction, with schemas and overheads
-- [Paper](reductions.pdf): definitions, constructions, and proofs
-- [Rust API](api/problemreductions/index.html): generated from source
+- [**Command line** install `pred`, then show, path, reduce and solve](cli.md)
+- [**Agent skills** workflows for proposing, implementing and reviewing rules](skills.md)
+- [**Rust library** models, reductions and solvers from code](getting-started.md)
+- [**Atlas** every variant and reduction, with schemas and overheads](index.html#atlas)
+- [**Paper** definitions, constructions, and proofs](reductions.pdf)
+- [**Rust API** generated from source](api/problemreductions/index.html)
 
 This guide covers the `pred` CLI, the agent skills shipped with the repository, and the Rust library. Every page has a **Markdown** link for reading without a browser; the [Markdown index](markdown/index.md) lists all pages.
 
diff --git a/docs/src/static/docs-theme.css b/docs/src/static/docs-theme.css
index 05d4adfa9..6d9ac784d 100644
--- a/docs/src/static/docs-theme.css
+++ b/docs/src/static/docs-theme.css
@@ -1,15 +1,8 @@
 @font-face {
   font-family: "DM Sans";
-  src: url("../../../assets/fonts/dm-sans-regular.ttf") format("truetype");
+  src: url("../../../assets/fonts/dm-sans-variable.woff2") format("woff2");
   font-style: normal;
-  font-weight: 400;
-  font-display: swap;
-}
-@font-face {
-  font-family: "DM Sans";
-  src: url("../../../assets/fonts/dm-sans-semibold.ttf") format("truetype");
-  font-style: normal;
-  font-weight: 600 800;
+  font-weight: 400 600;
   font-display: swap;
 }
 html[class] {
@@ -87,7 +80,7 @@ body {
 .chapter li a {
   display: block;
   padding: 7px 10px;
-  border-radius: 5px;
+  border-radius: 10px;
   color: var(--sidebar-fg);
 }
 .chapter li a:hover {
@@ -198,7 +191,7 @@ body {
 }
 .content code {
   font-size: 13px;
-  border-radius: 3px;
+  border-radius: 6px;
 }
 .content :not(pre) > code {
   background: #213025;
@@ -208,7 +201,7 @@ body {
 .content pre {
   margin: 20px 0;
   border: 1px solid #334437;
-  border-radius: 8px;
+  border-radius: 14px;
   background: #162019;
 }
 .content pre > code {
@@ -226,7 +219,7 @@ body {
 .content pre .buttons button {
   background: #233429;
   color: #d3dfcf;
-  border-radius: 4px;
+  border-radius: 8px;
   padding: 7px;
 }
 .content table {
@@ -254,11 +247,11 @@ body {
 .content blockquote {
   margin: 20px 0;
   padding: 8px 18px;
-  border-radius: 0 6px 6px 0;
+  border-radius: 0 10px 10px 0;
 }
 .content details {
   border: 1px solid #304034;
-  border-radius: 6px;
+  border-radius: 10px;
   padding: 12px 16px;
   margin: 18px 0;
 }
@@ -306,13 +299,13 @@ body {
   width: 100%;
   height: 490px;
   border: 1px solid #334437;
-  border-radius: 8px;
+  border-radius: 14px;
   background: #0d0f12;
   margin: 24px 0 16px;
 }
 :is(#searchbar, #mdbook-searchbar) {
   padding: 13px 16px;
-  border-radius: 6px;
+  border-radius: 10px;
 }
 :is(#search-wrapper, #mdbook-search-wrapper) {
   margin: 25px 0 0;
@@ -365,3 +358,44 @@ body {
     display: none;
   }
 }
+
+.docs-tools a[href$="graph.html"],
+.docs-tools a[href$="#atlas"],
+.docs-tools a[href$="#home"] {
+  color: var(--fg);
+}
+ul.start-cards {
+  display: grid;
+  grid-template-columns: repeat(auto-fill, minmax(230px, 1fr));
+  gap: 12px;
+  margin: 22px 0 8px;
+  padding: 0;
+  list-style: none;
+}
+.start-cards li {
+  margin: 0;
+}
+.content .start-cards a {
+  display: block;
+  height: 100%;
+  box-sizing: border-box;
+  padding: 14px 16px;
+  border: 1px solid var(--table-border-color);
+  border-radius: 14px;
+  background: var(--quote-bg);
+  color: var(--sidebar-fg);
+  font-size: 13px;
+  line-height: 1.5;
+  text-decoration: none;
+}
+.content .start-cards a:hover {
+  border-color: var(--links);
+}
+.start-cards a strong {
+  display: block;
+  color: var(--links);
+  font-size: 15px;
+}
+.content main > p:first-of-type {
+  max-width: 62ch;
+}
diff --git a/docs/src/static/docs-theme.js b/docs/src/static/docs-theme.js
index d984fc959..a6b9762f0 100644
--- a/docs/src/static/docs-theme.js
+++ b/docs/src/static/docs-theme.js
@@ -37,15 +37,19 @@
       resize();
     });
   }
+  if (page === "introduction.html" || page === "index.html")
+    document.querySelector(".content main > ul")?.classList.add("start-cards");
   const menu = document.querySelector(".menu-bar .right-buttons");
   if (menu && page !== "print.html") {
     const nav = document.createElement("nav");
     nav.className = "docs-tools";
     nav.setAttribute("aria-label", "Documentation resources");
     const links = [
-      ["Home ↗", root + "index.html#home"],
+      ["Home", root + "index.html#home"],
+      ["Graph", root + "graph.html"],
+      ["Atlas", root + "index.html#atlas"],
+      ["Paper ↗", root + "reductions.pdf"],
       ["GitHub ↗", "https://github.com/CodingThrust/problem-reductions"],
-      ["Atlas ↗", root + "index.html#atlas"],
     ];
     for (const [label, href] of links) {
       const link = document.createElement("a");
diff --git a/docs/website/README.md b/docs/website/README.md
index 164cdb213..cac875fc2 100644
--- a/docs/website/README.md
+++ b/docs/website/README.md
@@ -1,186 +1,38 @@
-# Research website
+# Website
 
-The public entry point presents Problem Reductions as infrastructure for autonomous
-research. It includes a searchable problem atlas, pages for every registered
-problem variant and reduction, and an interactive vertex-cover / independent-set
-example. Current implementation capabilities and future research ambitions are
-explicitly distinguished.
+Home/Atlas and the reduction graph use the Rust registry, WASM engine and Typst
+articles. Page code lives in `src/pages/`, the engine worker in `src/workers/`,
+and styles in `src/styles/`. Static data is validated during the build; generated
+TypeScript types describe the data consumed by the browser.
 
-The standalone `graph.html` is the primary visual explorer: the graph owns the
-workspace between a problem/rule browser and an always-visible detail panel.
-The browser lists registered families, expandable variants, and exact directed
-rules; its search and mode switch leave the graph viewport unchanged. Selecting
-an item highlights its graph counterpart.
-Drag the divider to resize the
-panel, or focus it and use the arrow keys (Home/End select the width limits).
-On narrow screens the panel sits below the graph.
-The fCoSE overview is computed at build time and published with the graph data,
-so reloads retain the same positions. Expanding variants relaxes the visible local
-neighborhood; collapsing restores the overview. Labels
-are culled by available screen space, with full variant labels reserved in layout.
-
-Details compile all problem definitions and reduction rules directly from
-`docs/paper/reductions.typ`, including their examples, footnotes and references.
-Graph's inspector and Atlas problem/reduction pages use the same renderer and
-article files. The inspector's “Open in Atlas” link retains exact variant
-endpoints; family-level selections open the corresponding default record.
-Selection stays at exact variant granularity: variant-specific content wins;
-otherwise the parent problem or directed problem-pair content is used by default.
-If neither exists, the panel explicitly reports missing documentation.
-No web prose is maintained separately. `problem-def` accepts `variant: (...)`;
-`reduction-rule` accepts `source-variant: (...)` and `target-variant: (...)` for
-specialized content. Omit these to publish shared family content.
-
-`scripts/build_graph_details.py` compiles once with Typst 0.15.1 and extracts
-each article into the release's `assets/details/` directory. The URL index and
-articles load on selection; the 24 most recently used articles are cached. References load
-when expanded. Repeated SVG glyph definitions are shared within each article.
-Generated content is not copied into the website source directory or committed.
-Text reflows in the panel; equations and figures use
-Typst's SVG rendering to preserve mathematical notation. The existing PDF build
-uses the same source and its original print presentation. HTML export remains
-experimental, so the build fails on export errors.
-
-## Build and preview
-
-Use mdBook 0.5.2 and Typst 0.15.1, matching the deployment workflow.
+Build and serve locally:
 
 ```sh
 make website
-python3 -m http.server 3001 --bind 127.0.0.1 --directory book
+python3 -m http.server 3001 --directory book
 ```
 
-Open <http://localhost:3001>. `make doc` also builds Rust API documentation.
-`make website`, `make doc`, and `make mdbook` share the `paper-data` prerequisite,
-which exports the `docs/paper/data/examples.json` that the Typst source reads.
-The deployment workflow builds the PDF and API and combines everything in `book/`.
-The fast `make website` preview includes the guide; API/PDF links require those
-additional builds, as in deployment.
-
-Website assets are published under `book/releases/<build-number>/assets/`.
-The builder rewrites their URLs together, so old open pages cannot mix new
-documentation with old registry data. If an old release is no longer available,
-reload the page. Do not overwrite files inside an existing release directory.
-The homepage loads a small registry summary; full Atlas data and the graph's
-local-layout library load only when needed.
-
-Finalization runs after PDF/API assembly. It externalizes generated inline
-scripts and applies a same-origin CSP (inline styles remain allowed for graph
-and Typst layout). Typst articles containing active elements, event handlers,
-or unsafe URLs fail the build. Deployment runs browser and build-security checks
-before upload; only the deploy job has Pages/OIDC write permissions.
-
-For CSS/JavaScript iteration after the registry exports have been generated:
+Frontend checks:
 
 ```sh
-python3 scripts/build_website.py
+npm ci
+npm run typecheck
+npm run lint:frontend
+npm run test:frontend-contracts
 ```
 
-The builder overlays the website's `index.html` and `assets/` onto mdBook's output.
-Existing documentation URLs, `introduction.html`, the paper, and Rust API paths
-stay available; the retired `reduction-graph.html` and `open-problems.html` redirect
-to their website counterparts through `[output.html.redirect]` in `book.toml`.
-Running `mdbook build` by itself restores mdBook's homepage; run
-the website builder afterward. The GitHub Pages workflow does this automatically.
-
-## Design and data
-
-- Deep forest surfaces, warm ivory text, and pale lime form the dark visual palette.
-- The header, footer, and favicon use the original `docs/logo.svg` artwork, recolored
-  at build time to match the dark palette. The canonical source logo stays unchanged.
-- Self-hosted DM Sans and Instrument Serif include their OFL licenses in `assets/fonts/`.
-- The graph is a generated SVG based on actual registry edges. Its homepage view
-  groups variants by problem family and does not imply that arbitrary paths compose.
-- Detail pages use exact variants. URLs encode problem names and variant keys,
-  rather than transient registry indices.
-- Model and rule “Open implementation” links follow GitHub `main`, not a pinned
-  commit. Source paths come from registry metadata and are checked against files
-  during the build; renamed files require a website rebuild and deployment.
-- Counts, schemas, capabilities, and overhead expressions come from the same
-  generated JSON used by the documentation and paper. Nothing is manually counted.
-- The five-vertex example is illustrative; research activity, novelty, and live test
-  results are never fabricated. A reduction's registration does not imply formal proof.
-- Navigation, filters, search, clipboard actions, and the example are keyboard
-  accessible. Layouts adapt to mobile; motion respects reduced-motion preferences.
-- No frontend framework or external font request is required. The graph uses
-  self-hosted Cytoscape and fCoSE; dependency licenses are copied beside the scripts.
-
-The static website does not yet provide agent execution, an experiment database,
-or live research telemetry. The research section describes the intended loop and
-links to the existing agent workflows.
-
-## Browser checks
-
-Build the documentation with `make doc` so API link checks have their targets,
-then build the PDF and run these commands with the preview server running:
-
-```sh
-typst compile --root . docs/paper/reductions.typ book/reductions.pdf
-uv run --no-project --with playwright==1.58.0 python -m playwright install chromium
-uv run --no-project --with playwright==1.58.0 python scripts/test_website.py
-```
-
-Set `WEBSITE_BROWSER_CHANNEL=chrome` to use an installed Chrome instead, or
-`WEBSITE_BASE_URL=http://localhost:3001/` to change the preview address. The suite
-exercises search, filters, exact variants, deep links, keyboard navigation,
-clipboard actions, the mathematical example, legacy docs, and mobile overflow.
-
-## Documentation
-
-The homepage and graph's **Open questions** link opens `open-questions/`.
-The board is generated from the registry and shared templates in
-[`GiggleLiu/autoresearch-gadgets`](https://github.com/GiggleLiu/autoresearch-gadgets),
-then included in the same Pages artifact. Legacy `#open-questions` and
-`open-problems.html` links redirect to the board.
-
-The deployment workflow reads that private repository's `main` branch with the
-existing `PROJECT_READ_TOKEN` secret. That token needs **Contents: read** access
-to `GiggleLiu/autoresearch-gadgets`; the default `GITHUB_TOKEN` cannot read another
-private repository. Only the generated `website/dist/` is published. Registry
-changes appear on the next documentation deployment; use **Run workflow** on
-`main` to refresh the board without changing this repository. Feature-branch
-runs build and verify the artifact without deploying it.
-
-To include the board in a local preview, clone its source beside this repository,
-build it with its committed lockfile, and run the website overlay after mdBook:
-
-```sh
-uv run --project ../autoresearch-gadgets/website --locked python ../autoresearch-gadgets/website/build.py
-python3 scripts/build_website.py --open-questions ../autoresearch-gadgets/website/dist
-```
-
-Include the board when running the browser suite. Without `--open-questions`,
-the builder previews the main website and guide only.
-
-The guide has seven pages listed in `docs/src/SUMMARY.md`: an overview, the CLI
-(quick start, command reference), agent skills, the Rust library
-(getting started, API, design). Keep one example per
-concept and link to `pred --help`, rustdoc, or `.claude/CLAUDE.md` instead of
-restating them.
-
-`docs/src/static/docs-theme.css` supplies the restrained dark reading theme;
-`docs-theme.js` adds the GitHub and atlas links. Native mdBook search, code copying, and
-sidebar navigation remain available. Both mdBook 0.4.37 and 0.5.2 (deployment)
-are supported.
-
-The website builder emits `book/markdown/` from the same source pages, expanding
-Rust and generated-output includes. The Markdown index is the entry point for
-agents.
-
-## CLI recording
-
-`docs/src/static/cli-demo.cast` contains real PTY output from six successful
-commands against the current CLI. `cli-demo.html` embeds a copy of that cast
-and asciinema-player 3.8.0 for offline playback, with autoplay disabled; the
-recording script refreshes both files. The bundled
-player is Apache-2.0 licensed; its license is alongside the recording.
+Types and Rust schemas are regenerated automatically by the checks and website
+build into the ignored `src/generated/` directory. The five static-data schemas
+are maintained here; build-only validation runs in `scripts/website_contracts.mjs`.
 
-To refresh the recording after a CLI change, build the CLI and run:
+For a fresh production build tested in Chromium, Firefox and WebKit:
 
 ```sh
-python3 scripts/record_cli_demo.py --pred target/debug/pred
+uv run --python 3.12.14 --no-project --with-requirements scripts/website-requirements.txt python -m playwright install chromium firefox webkit
+uv run --python 3.12.14 --no-project --with-requirements scripts/website-requirements.txt python scripts/check_website.py
 ```
 
-The script runs the commands listed in `docs/src/cli.md` in a temporary
-directory, simulates typing, and fails if any command exits non-zero. Never
-substitute a simulated successful run.
+The verifier prints its temporary output directory. Use `--output /tmp/new-site`
+to choose one, or `--site /path/to/site` to test an existing build. The optional
+Open Question Board is supplied with `--open-questions /path/to/board`.
+Deploy the complete generated site so HTML, data, scripts and WASM stay together.
diff --git a/docs/website/assets/details.js b/docs/website/assets/details.js
deleted file mode 100644
index e6539b06a..000000000
--- a/docs/website/assets/details.js
+++ /dev/null
@@ -1,161 +0,0 @@
-(() => {
-  "use strict";
-  const detailCache = new Map();
-  let manifest;
-  let renderRequest = 0;
-  function loadDetail(key) {
-    const url = window.GRAPH_DETAILS.entries[key];
-    if (!url) return Promise.reject(new Error(`Missing detail file: ${key}`));
-    if (!detailCache.has(url)) {
-      detailCache.set(url, fetch(url).then((response) => {
-        if (!response.ok) throw new Error(`Cannot load documentation (${response.status})`);
-        return response.text();
-      }).catch((error) => {
-        detailCache.delete(url);
-        throw error;
-      }));
-      if (detailCache.size > 24) detailCache.delete(detailCache.keys().next().value);
-    } else {
-      const cached = detailCache.get(url);
-      detailCache.delete(url);
-      detailCache.set(url, cached);
-    }
-    return detailCache.get(url);
-  }
-
-  window.renderDetails = async function(detail, title, variant, key, parentKey, onProblem) {
-    const request = ++renderRequest;
-    detail.replaceChildren();
-    detail.onclick = (event) => {
-      const link = event.target.closest('a[href^="#"]');
-      if (!link) return;
-      const anchor = link.hash.slice(1);
-      const key = window.GRAPH_DETAILS.anchors[anchor];
-      if (key?.startsWith("problem:") && key !== detail.querySelector("article")?.dataset.contentKey) {
-        event.preventDefault();
-        onProblem(key.slice("problem:".length));
-        return;
-      }
-      if (link.getAttribute("role") === "doc-biblioref") {
-        event.preventDefault();
-        const references = detail.querySelector(".detail-references");
-        references.open = true;
-        references.scrollIntoView({ block: "nearest" });
-        return;
-      }
-      const target = detail.querySelector(`[id="${CSS.escape(link.hash.slice(1))}"]`);
-      if (!target) {
-        if (key === detail.querySelector("article")?.dataset.contentKey) {
-          event.preventDefault();
-          detail.scrollIntoView({ block: "start" });
-        }
-        return;
-      }
-      event.preventDefault();
-      const references = target.closest("details");
-      if (references) references.open = true;
-      target.scrollIntoView({ block: "nearest" });
-    };
-
-    if (title) {
-      const heading = document.createElement("h2");
-      heading.textContent = title;
-      detail.append(heading);
-    }
-    if (variant) {
-      const parameters = document.createElement("p");
-      parameters.className = "detail-variant";
-      parameters.textContent = variant;
-      detail.append(parameters);
-    }
-    const article = document.createElement("article");
-    article.className = "typst-detail";
-    article.textContent = "Loading documentation…";
-    detail.append(article);
-    if (!window.GRAPH_DETAILS) {
-      try {
-        manifest ||= fetch("./assets/graph-details.json").then(response => {
-          if (!response.ok) throw new Error("Cannot load documentation index. Reload the page to get the current release.");
-          return response.json();
-        });
-        window.GRAPH_DETAILS = await manifest;
-      } catch (error) {
-        manifest = null;
-        if (request === renderRequest) {
-          article.textContent = error.message;
-          article.setAttribute("role", "alert");
-        }
-        return;
-      }
-    }
-    if (request !== renderRequest || !article.isConnected) return;
-    const contentKey = window.GRAPH_DETAILS.entries[key] ? key : parentKey;
-    const available = Boolean(window.GRAPH_DETAILS.entries[contentKey]);
-    if (!available) {
-      const note = document.createElement("p");
-      note.className = "detail-source";
-      note.textContent = "No documentation is available for this entry or its parent family.";
-      detail.append(note);
-    }
-    article.dataset.contentKey = contentKey;
-    if (available) {
-      article.textContent = "Loading documentation…";
-      article.setAttribute("aria-busy", "true");
-    }
-    if (!available) { article.remove(); return; }
-    try {
-      const content = await loadDetail(contentKey);
-      if (!article.isConnected) return;
-      // HTML is generated at build time from the repository's Typst source.
-      article.innerHTML = content;
-      const citations = new Set([...article.querySelectorAll('a[role="doc-biblioref"]')]
-        .map((link) => link.hash.slice(1)));
-      if (citations.size) {
-        const references = document.createElement("details");
-        references.className = "detail-references";
-        references.innerHTML = "<summary>References</summary><div></div>";
-        article.after(references);
-        const body = references.lastElementChild;
-        let loaded = false;
-        references.addEventListener("toggle", async () => {
-          if (!references.open || loaded) return;
-          body.textContent = "Loading references…";
-          try {
-            body.innerHTML = await loadDetail("references");
-            body.querySelectorAll("li").forEach((item) => {
-              if (!citations.has(item.id)) item.remove();
-            });
-            loaded = true;
-          } catch (error) {
-            body.textContent = error.message;
-            body.setAttribute("role", "alert");
-          }
-        });
-      }
-      if (article.querySelector('[role="doc-noteref"] a')) {
-        const notes = document.createElement("aside");
-        notes.className = "typst-detail detail-footnotes";
-        try {
-          notes.innerHTML = await loadDetail("footnotes");
-          const used = new Set([...article.querySelectorAll('[role="doc-noteref"] a')].map((link) => link.hash.slice(1)));
-          notes.querySelectorAll('li').forEach((item) => {
-            if (!used.has(item.id)) item.remove();
-          });
-        } catch (error) {
-          // The article is already rendered; only its footnotes degrade.
-          notes.textContent = error.message;
-          notes.setAttribute("role", "alert");
-        }
-        if (!article.isConnected) return;
-        article.after(notes);
-      }
-    } catch (error) {
-      if (!article.isConnected) return;
-      article.textContent = error.message;
-      article.setAttribute("role", "alert");
-    } finally {
-      article.removeAttribute("aria-busy");
-    }
-  }
-
-})();
diff --git a/docs/website/assets/fonts/DM-Sans-OFL.txt b/docs/website/assets/fonts/DM-Sans-OFL.txt
deleted file mode 100644
index a0eedfbf0..000000000
--- a/docs/website/assets/fonts/DM-Sans-OFL.txt
+++ /dev/null
@@ -1,93 +0,0 @@
-Copyright 2014 The DM Sans Project Authors (https://github.com/googlefonts/dm-fonts)
-
-This Font Software is licensed under the SIL Open Font License, Version 1.1.
-This license is copied below, and is also available with a FAQ at:
-https://scripts.sil.org/OFL
-
-
------------------------------------------------------------
-SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
------------------------------------------------------------
-
-PREAMBLE
-The goals of the Open Font License (OFL) are to stimulate worldwide
-development of collaborative font projects, to support the font creation
-efforts of academic and linguistic communities, and to provide a free and
-open framework in which fonts may be shared and improved in partnership
-with others.
-
-The OFL allows the licensed fonts to be used, studied, modified and
-redistributed freely as long as they are not sold by themselves. The
-fonts, including any derivative works, can be bundled, embedded,
-redistributed and/or sold with any software provided that any reserved
-names are not used by derivative works. The fonts and derivatives,
-however, cannot be released under any other type of license. The
-requirement for fonts to remain under this license does not apply
-to any document created using the fonts or their derivatives.
-
-DEFINITIONS
-"Font Software" refers to the set of files released by the Copyright
-Holder(s) under this license and clearly marked as such. This may
-include source files, build scripts and documentation.
-
-"Reserved Font Name" refers to any names specified as such after the
-copyright statement(s).
-
-"Original Version" refers to the collection of Font Software components as
-distributed by the Copyright Holder(s).
-
-"Modified Version" refers to any derivative made by adding to, deleting,
-or substituting -- in part or in whole -- any of the components of the
-Original Version, by changing formats or by porting the Font Software to a
-new environment.
-
-"Author" refers to any designer, engineer, programmer, technical
-writer or other person who contributed to the Font Software.
-
-PERMISSION & CONDITIONS
-Permission is hereby granted, free of charge, to any person obtaining
-a copy of the Font Software, to use, study, copy, merge, embed, modify,
-redistribute, and sell modified and unmodified copies of the Font
-Software, subject to the following conditions:
-
-1) Neither the Font Software nor any of its individual components,
-in Original or Modified Versions, may be sold by itself.
-
-2) Original or Modified Versions of the Font Software may be bundled,
-redistributed and/or sold with any software, provided that each copy
-contains the above copyright notice and this license. These can be
-included either as stand-alone text files, human-readable headers or
-in the appropriate machine-readable metadata fields within text or
-binary files as long as those fields can be easily viewed by the user.
-
-3) No Modified Version of the Font Software may use the Reserved Font
-Name(s) unless explicit written permission is granted by the corresponding
-Copyright Holder. This restriction only applies to the primary font name as
-presented to the users.
-
-4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font
-Software shall not be used to promote, endorse or advertise any
-Modified Version, except to acknowledge the contribution(s) of the
-Copyright Holder(s) and the Author(s) or with their explicit written
-permission.
-
-5) The Font Software, modified or unmodified, in part or in whole,
-must be distributed entirely under this license, and must not be
-distributed under any other license. The requirement for fonts to
-remain under this license does not apply to any document created
-using the Font Software.
-
-TERMINATION
-This license becomes null and void if any of the above conditions are
-not met.
-
-DISCLAIMER
-THE FONT SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
-EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF
-MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT
-OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE
-COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
-INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL
-DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
-FROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM
-OTHER DEALINGS IN THE FONT SOFTWARE.
diff --git a/docs/website/assets/fonts/Instrument-Serif-OFL.txt b/docs/website/assets/fonts/OFL.txt
similarity index 91%
rename from docs/website/assets/fonts/Instrument-Serif-OFL.txt
rename to docs/website/assets/fonts/OFL.txt
index e1801b959..8cf401f79 100644
--- a/docs/website/assets/fonts/Instrument-Serif-OFL.txt
+++ b/docs/website/assets/fonts/OFL.txt
@@ -1,9 +1,10 @@
+Copyright 2020 The DM Mono Project Authors (https://www.github.com/googlefonts/dm-mono)
+Copyright 2014 The DM Sans Project Authors (https://github.com/googlefonts/dm-fonts)
 Copyright 2022 The Instrument Serif Project Authors (https://github.com/Instrument/instrument-serif)
 
-This Font Software is licensed under the SIL Open Font License, Version 1.1.
-This license is copied below, and is also available with a FAQ at:
-https://scripts.sil.org/OFL
-
+These fonts (DM Mono, DM Sans and Instrument Serif) are each licensed under the
+SIL Open Font License, Version 1.1. The license is copied below, and is also
+available with a FAQ at: https://openfontlicense.org
 
 -----------------------------------------------------------
 SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
diff --git a/docs/website/assets/fonts/dm-mono-medium.woff2 b/docs/website/assets/fonts/dm-mono-medium.woff2
new file mode 100644
index 000000000..48879e4e9
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diff --git a/docs/website/assets/fonts/dm-mono-regular.woff2 b/docs/website/assets/fonts/dm-mono-regular.woff2
new file mode 100644
index 000000000..787b808fd
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diff --git a/docs/website/assets/fonts/dm-sans-regular.ttf b/docs/website/assets/fonts/dm-sans-regular.ttf
deleted file mode 100644
index 6c789eadb..000000000
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diff --git a/docs/website/assets/fonts/dm-sans-semibold.ttf b/docs/website/assets/fonts/dm-sans-semibold.ttf
deleted file mode 100644
index ec5dcf3e2..000000000
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diff --git a/docs/website/assets/fonts/dm-sans-variable.woff2 b/docs/website/assets/fonts/dm-sans-variable.woff2
new file mode 100644
index 000000000..8f8cb5508
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diff --git a/docs/website/assets/fonts/instrument-serif-italic.ttf b/docs/website/assets/fonts/instrument-serif-italic.ttf
deleted file mode 100644
index 25d2a8219..000000000
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diff --git a/docs/website/assets/fonts/instrument-serif-italic.woff2 b/docs/website/assets/fonts/instrument-serif-italic.woff2
new file mode 100644
index 000000000..a49ad2bd9
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diff --git a/docs/website/assets/fonts/instrument-serif.ttf b/docs/website/assets/fonts/instrument-serif.ttf
deleted file mode 100644
index 8794c6950..000000000
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diff --git a/docs/website/assets/fonts/instrument-serif.woff2 b/docs/website/assets/fonts/instrument-serif.woff2
new file mode 100644
index 000000000..d5315b531
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diff --git a/docs/website/assets/graph.css b/docs/website/assets/graph.css
deleted file mode 100644
index 952bb59d9..000000000
--- a/docs/website/assets/graph.css
+++ /dev/null
@@ -1,352 +0,0 @@
-.graph-page {
-  height: 100vh;
-  overflow: hidden;
-}
-
-.graph-page .site-header {
-  position: relative;
-}
-
-.graph-header {
-  width: calc(100% - 40px);
-  max-width: none;
-  height: 70px;
-}
-
-.graph-header .project-logo {
-  width: 215px;
-}
-
-.graph-header nav {
-  flex-shrink: 0;
-}
-
-.graph-search {
-  width: min(560px, 42vw);
-  margin-left: auto;
-}
-
-#reduction-graph {
-  height: calc(100vh - 70px);
-  min-height: 620px;
-  display: grid;
-  grid-template-rows: 48px minmax(0, 1fr);
-  background: #0d1410;
-}
-
-#reduction-graph:focus {
-  outline: none;
-}
-
-.graph-toolbar {
-  display: flex;
-  align-items: center;
-  justify-content: space-between;
-  gap: 24px;
-  padding: 0 20px;
-  border-bottom: 1px solid var(--line);
-  background: #111a15;
-  font-size: 14px;
-}
-
-.graph-toolbar > div:first-child {
-  display: flex;
-  align-items: baseline;
-  gap: 14px;
-}
-
-.graph-toolbar strong {
-  color: var(--ink);
-  font-weight: 600;
-}
-
-.graph-toolbar span {
-  color: #718075;
-}
-
-.graph-view-controls {
-  display: flex;
-  align-self: stretch;
-}
-
-.graph-view-controls button {
-  padding: 0 14px;
-  color: var(--muted);
-  background: transparent;
-  border: 0;
-  border-left: 1px solid var(--line);
-  font-size: 14px;
-}
-
-.graph-view-controls button[aria-pressed="true"] {
-  color: var(--green);
-  background: #17231b;
-}
-
-.graph-view-controls button:hover {
-  color: var(--ink);
-}
-
-.graph-workspace {
-  min-height: 0;
-  display: grid;
-  grid-template-columns: 260px minmax(0, 1fr) 8px clamp(240px, var(--inspector-width, 320px), calc((100% - 260px) * 0.6));
-}
-
-.graph-browser {
-  min-height: 0;
-  display: flex;
-  flex-direction: column;
-  background: #111a15;
-  border-right: 1px solid var(--line);
-}
-.browser-modes { display: flex; padding: 14px 14px 10px; gap: 6px; }
-.browser-modes button {
-  flex: 1; padding: 9px; border: 1px solid var(--line); border-radius: 5px;
-  background: transparent; color: var(--muted); font-size: 14px;
-}
-.browser-modes button[aria-pressed="true"] { background: #273622; color: var(--green); }
-#browser-search {
-  min-width: 0; margin: 0 14px; padding: 10px; border: 1px solid var(--line);
-  border-radius: 4px; background: #0d1410; color: var(--ink); font-size: 15px;
-}
-#browser-count { margin: 12px 16px; color: var(--muted); font-size: 13px; }
-#browser-list { min-height: 0; flex: 1; overflow-y: auto; }
-.browser-item {
-  display: block; width: 100%; padding: 12px 16px; border: 0;
-  border-bottom: 1px solid var(--line); background: transparent;
-  color: var(--ink); text-align: left; font-size: 15px; overflow-wrap: anywhere;
-}
-.browser-item small { display: block; margin-top: 5px; color: var(--muted); font-size: 13px; line-height: 1.6; }
-.browser-item:hover { background: #1b281f; }
-.browser-item[aria-current="true"] { background: #35492c; color: #f0f6e9; box-shadow: inset 4px 0 #c4dda6; }
-.browser-item[aria-current="true"] small { color: #c5d3bc; }
-.browser-item.variant-item { padding-left: 28px; color: #c4dda6; }
-.browser-empty { padding: 16px; color: var(--muted); font-size: 13px; }
-
-.graph-inspector {
-  min-width: 0;
-  overflow-y: auto;
-  background: #111a15;
-}
-
-.graph-divider {
-  cursor: col-resize;
-  touch-action: none;
-  background: #111a15;
-  border-inline: 1px solid var(--line);
-}
-
-.graph-divider:hover,
-.graph-divider:focus-visible,
-.graph-divider.dragging {
-  background: #748d67;
-  outline: none;
-}
-
-.inspector-heading {
-  height: 56px;
-  display: flex;
-  align-items: center;
-  justify-content: space-between;
-  padding: 0 18px;
-  border-bottom: 1px solid var(--line);
-}
-
-.inspector-heading span {
-  color: #87958a;
-  font-size: 14px;
-}
-
-.graph-detail { padding: 22px 20px 28px; font-size: 16px; line-height: 1.7; }
-.graph-detail:empty { padding: 0; }
-.graph-detail h2 { margin: 0 0 10px; font-size: 21px; line-height: 1.35; font-weight: 500; overflow-wrap: anywhere; }
-
-.graph-canvas {
-  min-width: 0;
-  min-height: 0;
-  position: relative;
-  overflow: hidden;
-  background-color: #0d1410;
-  background-image: radial-gradient(#243329 0.7px, transparent 0.7px);
-  background-size: 19px 19px;
-}
-
-#cy {
-  width: 100%;
-  height: 100%;
-}
-#cy[aria-busy="true"] { visibility: hidden; }
-
-.graph-legend {
-  position: absolute;
-  left: 18px;
-  max-width: calc(100% - 36px);
-  bottom: 17px;
-  display: flex;
-  flex-wrap: wrap;
-  pointer-events: none;
-  gap: 13px;
-  padding: 9px 12px;
-  color: #91a095;
-  background: rgba(13, 20, 16, 0.9);
-  border: 1px solid var(--line);
-  border-radius: 5px;
-  backdrop-filter: blur(10px);
-  font-size: 13px;
-}
-
-.graph-legend span {
-  display: flex;
-  align-items: center;
-  gap: 5px;
-}
-
-.graph-legend i {
-  width: 7px;
-  height: 7px;
-  border-radius: 50%;
-  background: var(--category-color);
-}
-
-.category-graph {
-  --category-color: #b9d99b;
-}
-.category-formula {
-  --category-color: #9bbfc0;
-}
-.category-set {
-  --category-color: #d1a78d;
-}
-.category-algebraic {
-  --category-color: #d8c87e;
-}
-.category-misc {
-  --category-color: #bd9dbc;
-}
-
-.graph-canvas-note {
-  position: absolute;
-  top: 18px;
-  right: 18px;
-  max-width: calc(100% - 36px);
-  margin: 0;
-  text-align: right;
-  color: #68766c;
-  font-size: 13px;
-  pointer-events: none;
-}
-
-.graph-detail {
-  padding: 24px 22px 34px;
-}
-
-.graph-tooltip {
-  max-width: 260px;
-  display: none;
-  position: fixed;
-  z-index: 50;
-  padding: 8px 10px;
-  color: var(--ink);
-  background: rgba(21, 32, 25, 0.96);
-  border: 1px solid #465b49;
-  border-radius: 4px;
-  box-shadow: 0 12px 35px rgba(0, 0, 0, 0.3);
-  font-size: 14px;
-  pointer-events: none;
-}
-
-@media (max-width: 1100px) {
-  .graph-header nav .docs-nav {
-    display: none;
-  }
-  .graph-canvas-note {
-    display: none;
-  }
-}
-
-@media (max-width: 800px) {
-  .graph-page {
-    height: auto;
-    overflow: auto;
-  }
-  .graph-header {
-    min-height: 118px;
-  }
-  .graph-header .graph-search {
-    width: calc(100% - 230px);
-    order: 2;
-  }
-  .graph-header nav {
-    order: 3;
-  }
-  #reduction-graph {
-    height: auto;
-    min-height: 0;
-  }
-  .graph-toolbar {
-    min-height: 62px;
-    padding-block: 8px;
-  }
-  .graph-toolbar > div:first-child span {
-    display: none;
-  }
-  .graph-workspace {
-    grid-template-columns: 1fr;
-    grid-template-rows: 280px 62vh auto;
-  }
-  .graph-browser { grid-row: 1; border-right: 0; border-bottom: 1px solid var(--line); }
-  .graph-divider {
-    display: none;
-  }
-  .graph-canvas {
-    grid-row: 2;
-  }
-  .graph-inspector {
-    grid-row: 3;
-    min-height: 180px;
-    border-left: 0;
-    border-top: 1px solid var(--line);
-  }
-}
-
-@media (max-width: 520px) {
-  .graph-header .project-logo {
-    width: 185px;
-  }
-  .graph-header .graph-search {
-    width: 100%;
-    order: 3;
-  }
-  .graph-header nav {
-    order: 2;
-    width: auto;
-    gap: 16px;
-  }
-  .graph-header nav .docs-nav {
-    display: none;
-  }
-  .graph-toolbar {
-    align-items: flex-start;
-    flex-direction: column;
-    gap: 7px;
-  }
-  #reduction-graph {
-    grid-template-rows: auto minmax(0, 1fr);
-  }
-  .graph-view-controls {
-    width: 100%;
-    min-height: 38px;
-  }
-  .graph-view-controls button {
-    flex: 1;
-    padding: 0 6px;
-    border: 1px solid var(--line);
-  }
-  .graph-legend {
-    right: 12px;
-    left: 12px;
-    max-width: none;
-    justify-content: center;
-  }
-}
diff --git a/docs/website/assets/graph.js b/docs/website/assets/graph.js
deleted file mode 100644
index ba6b5ec2d..000000000
--- a/docs/website/assets/graph.js
+++ /dev/null
@@ -1,853 +0,0 @@
-(async () => {
-  "use strict";
-
-  try {
-      const data = window.REDUCTIONS;
-      if (!data) throw new Error("Cannot load graph data. Reload the page to get the current release.");
-      const schemas = new Map(data.schemas.map((schema) => [schema.name, schema]));
-      const aliases = new Map([
-        ["MIS", "MaximumIndependentSet"],
-        ["MVC", "MinimumVertexCover"],
-        ["SAT", "Satisfiability"],
-        ["3SAT", "KSatisfiability"],
-        ["3-SAT", "KSatisfiability"],
-      ]);
-      const colors = {
-        graph: "#b9d99b",
-        formula: "#9bbfc0",
-        set: "#d1a78d",
-        algebraic: "#d8c87e",
-        misc: "#bd9dbc",
-      };
-      const families = new Map();
-
-      data.nodes.forEach((node) => {
-        const family = families.get(node.name) || {
-          name: node.name,
-          category: node.category,
-          variants: [],
-          incoming: new Set(),
-          outgoing: new Set(),
-          rules: 0,
-        };
-        family.variants.push(node);
-        families.set(node.name, family);
-      });
-
-      const connections = new Map();
-      data.edges.forEach((edge) => {
-        const source = data.nodes[edge.source].name;
-        const target = data.nodes[edge.target].name;
-        if (source === target) return;
-        const key = `${source}\u0000${target}`;
-        const connection = connections.get(key) || { source, target, count: 0 };
-        connection.count += 1;
-        connections.set(key, connection);
-        families.get(source).outgoing.add(target);
-        families.get(target).incoming.add(source);
-        families.get(source).rules += 1;
-        families.get(target).rules += 1;
-      });
-
-      const displayName = (name) =>
-        schemas.get(name)?.display_name ||
-        name
-          .replace(/([a-z0-9])([A-Z])/g, "$1 $2")
-          .replace(/([A-Z])([A-Z][a-z])/g, "$1 $2");
-
-      const variantKey = (variant) =>
-        Object.entries(variant)
-          .sort(([a], [b]) => a.localeCompare(b))
-          .map(([key, value]) => `${key}=${value}`)
-          .join(",");
-
-      const search = document.querySelector("#graph-search");
-      const inspector = document.querySelector(".graph-inspector");
-      const selectionType = document.querySelector("#selection-type");
-      const detail = document.querySelector("#graph-detail");
-      const tooltip = document.querySelector("#graph-tooltip");
-      let scope = "core";
-
-      const elements = [];
-      families.forEach((family) => {
-        const neighbors = new Set([...family.incoming, ...family.outgoing]);
-        const position = data.layout[family.name];
-        if (!position) throw new Error(`Missing graph layout position: ${family.name}`);
-        elements.push({
-          data: {
-            id: family.name,
-            label: displayName(family.name),
-            category: family.category,
-            rules: family.rules,
-            peripheral: neighbors.size < 2,
-          },
-          position: { x: position.x * 1.15, y: position.y * 1.15 },
-        });
-      });
-      connections.forEach((connection) =>
-        elements.push({
-          data: {
-            id: `edge:${connection.source}:${connection.target}`,
-            source: connection.source,
-            target: connection.target,
-            count: connection.count,
-          },
-        }),
-      );
-
-      const cy = cytoscape({
-        container: document.querySelector("#cy"),
-        elements: [],
-        layout: { name: "preset" },
-        minZoom: 0.08,
-        maxZoom: 3,
-        wheelSensitivity: 0.22,
-        boxSelectionEnabled: false,
-        style: [
-          {
-            selector: "node",
-            style: {
-              width: (node) => Math.min(22, 10 + Math.log2(1 + node.data("rules")) * 1.5),
-              height: (node) => Math.min(22, 10 + Math.log2(1 + node.data("rules")) * 1.5),
-              shape: "ellipse",
-              "background-color": (node) =>
-                colors[node.data("category")] || colors.misc,
-              "border-color": "#0d1410",
-              "border-width": 2,
-              label: "",
-              color: "#b9c4bb",
-              "font-family": "DM Sans, sans-serif",
-              "font-size": 12,
-              "font-weight": 400,
-              "min-zoomed-font-size": 7,
-              "text-valign": "bottom",
-              "text-margin-y": 8,
-              "text-background-color": "#0d1410",
-              "text-background-opacity": 0.72,
-              "text-background-padding": 2,
-              cursor: "pointer",
-            },
-          },
-          {
-            selector: "node.named",
-            style: { label: "data(label)" },
-          },
-          {
-            selector: "edge",
-            style: {
-              width: 0.9,
-              "line-color": "#8fa992",
-              "target-arrow-shape": "none",
-              "mid-target-arrow-shape": "none",
-              "mid-target-arrow-color": "#d2e4bd",
-              "arrow-scale": 0.7,
-              "curve-style": "bezier",
-              opacity: 0.45,
-              cursor: "pointer",
-            },
-          },
-          { selector: ".core-hidden", style: { display: "none" } },
-          {
-            selector: ".faded",
-            style: { opacity: 0.045, "text-opacity": 0 },
-          },
-          {
-            selector: "node.selected",
-            style: {
-              label: "data(label)",
-              "background-color": "#e1f1c9",
-              "border-color": "#5c7957",
-              "border-width": 2,
-              color: "#eef4ea",
-              "font-size": 12,
-              "text-opacity": 1,
-              "z-index": 20,
-            },
-          },
-          {
-            selector: "edge.selected",
-            style: {
-              "line-color": "#c4dda6",
-              "mid-target-arrow-shape": "triangle",
-              width: 1.2,
-              opacity: 0.95,
-              "z-index": 18,
-            },
-          },
-          {
-            selector: "node.neighbor",
-            style: { label: "", opacity: 0.8, width: 13, height: 13 },
-          },
-          {
-            selector: "node.expanded",
-            style: {
-              shape: "round-rectangle",
-              label: "data(label)",
-              "background-opacity": 0.8,
-              "background-color": "#0d1410",
-              "border-color": "#344739",
-              "border-width": 1,
-              "text-valign": "top",
-              "text-margin-y": -10,
-              padding: 24,
-            },
-          },
-          {
-            selector: "node[?isVariant]",
-            style: {
-              label: "data(label)",
-              shape: "ellipse",
-              width: 20,
-              height: 20,
-              "text-valign": "bottom",
-              "text-margin-y": 10,
-              "text-wrap": "wrap",
-              "text-max-width": 145,
-              "font-size": 14,
-              color: "#d6e2d1",
-              "border-width": 2,
-              "text-background-opacity": 1,
-            },
-          },
-          { selector: ".focus-hidden", style: { display: "none" } },
-          {
-            selector: "node.hovered, node.named",
-            style: { label: "data(label)", "text-opacity": 1, "z-index": 30 },
-          },
-          {
-            selector: "edge.hovered, edge.direction",
-            style: {
-              "mid-target-arrow-shape": "triangle",
-              "line-color": "#b6c9a7",
-              opacity: 0.9,
-              width: 1.3,
-            },
-          },
-          {
-            selector: "node.search-match",
-            style: {
-              label: "data(label)",
-              "background-color": "#e1f1c9",
-              "border-color": "#8eaa7f",
-              "border-width": 4,
-              opacity: 1,
-              "text-opacity": 1,
-              "z-index": 20,
-            },
-          },
-        ],
-      });
-
-      search.disabled = true;
-      for (let index = 0; index < elements.length; index += 40) {
-        cy.batch(() => cy.add(elements.slice(index, index + 40)));
-        await new Promise(resolve => setTimeout(resolve, 0));
-      }
-
-      function relax(elements) {
-        const variants = elements.nodes("[?isVariant]");
-        // Reserve the full two-line label footprint while solving, then draw compact dots.
-        variants.style({ width: 180, height: 120, label: "" });
-        elements.layout({
-          ...reductionLayoutOptions,
-          idealEdgeLength: 95,
-          edgeElasticity: 0.45,
-        }).run();
-        variants.removeStyle("width height label");
-      }
-      const expanded = new Set();
-      const browserSearch = document.querySelector("#browser-search");
-      const browserList = document.querySelector("#browser-list");
-      let browseMode = "problems";
-      let selectedProblem = "";
-      let selectedRules = new Set();
-      const overviewPositions = new Map(cy.nodes().map((node) => [node.id(), { ...node.position() }]));
-      const variantId = (node) => `${node.name}/${variantKey(node.variant)}`;
-      const describeVariant = (node) => Object.entries(node.variant)
-        .map(([key, value]) => `${key}: ${value}`).join(", ") || "Default variant";
-
-      function showDetails(title, variant, key, parentKey) {
-        inspector.scrollTop = 0;
-        window.renderDetails(detail, title, variant, key, parentKey, (problem) => {
-          transition(() => selectNode(cy.getElementById(problem.split("/")[0])));
-        });
-        const atlas = document.createElement("a");
-        atlas.className = "detail-atlas";
-        atlas.textContent = "Open in Atlas ↗";
-        const endpoint = (value) => {
-          const [name, variant = ""] = value.split("/");
-          return [encodeURIComponent(name), encodeURIComponent(variant)];
-        };
-        if (key.startsWith("problem:")) {
-          const [name, variant] = endpoint(key.slice(8));
-          atlas.href = `./index.html#problem/${name}${variant ? `?variant=${variant}` : ""}`;
-        } else {
-          const [source, target] = key.slice(5).split("->").map(endpoint);
-          atlas.href = `./index.html#reduction/${source[0]}/${target[0]}${key.includes("/") ? `?from=${source[1]}&to=${target[1]}` : ""}`;
-        }
-        detail.querySelector("h2").after(atlas);
-        const pdf = document.createElement("a");
-        pdf.href = "./reductions.pdf";
-        pdf.target = "_blank";
-        pdf.rel = "noopener";
-        pdf.className = "detail-pdf";
-        pdf.textContent = "Open PDF reference ↗";
-        detail.append(pdf);
-      }
-
-      const reducedMotion = window.matchMedia("(prefers-reduced-motion: reduce)");
-      let finishMotion;
-      let layoutLoaded;
-      let transitionRequest = 0;
-
-      async function transition(change) {
-        const request = ++transitionRequest;
-        try {
-          layoutLoaded ||= new Promise((resolve, reject) => {
-            const script = document.createElement("script");
-            script.src = "./assets/layout-bundle.js";
-            script.onload = resolve;
-            script.onerror = () => reject(new Error("Cannot load graph layout. Reload the page to get the current release."));
-            document.head.append(script);
-          });
-          await layoutLoaded;
-        } catch (error) {
-          layoutLoaded = null;
-          detail.textContent = error.message;
-          detail.setAttribute("role", "alert");
-          return;
-        }
-        if (request !== transitionRequest) return;
-        if (finishMotion) finishMotion();
-        if (reducedMotion.matches) {
-          change();
-          return;
-        }
-        const before = new Map(cy.nodes().map((node) => [node.id(), {
-          position: { ...node.position() }, data: { ...node.data() },
-        }]));
-        const fromView = { zoom: cy.zoom(), pan: { ...cy.pan() } };
-        change();
-        const toView = { zoom: cy.zoom(), pan: { ...cy.pan() } };
-        const moving = cy.nodes().not(":parent").map((node) => ({
-          node,
-          from: before.get(node.id())?.position || before.get(node.data("parent")).position,
-          to: { ...node.position() },
-        }));
-        const exiting = [];
-        before.forEach(({ data, position }, id) => {
-          if (!data.isVariant || cy.getElementById(id).nonempty()) return;
-          const target = cy.getElementById(data.parent).position();
-          const ghostData = { ...data };
-          delete ghostData.parent;
-          const ghost = cy.add({ data: ghostData, position, classes: "exiting" });
-          ghost.style("events", "no");
-          exiting.push(ghost);
-          moving.push({ node: ghost, from: position, to: { ...target } });
-        });
-        const mix = (a, b, t) => a + (b - a) * t;
-        let frame;
-        function draw(t) {
-          cy.batch(() => {
-            moving.forEach(({ node, from, to }) => node.position({
-              x: mix(from.x, to.x, t), y: mix(from.y, to.y, t),
-            }));
-            exiting.forEach((node) => node.style("opacity", 1 - t));
-          });
-          cy.viewport({ zoom: mix(fromView.zoom, toView.zoom, t), pan: {
-            x: mix(fromView.pan.x, toView.pan.x, t),
-            y: mix(fromView.pan.y, toView.pan.y, t),
-          } });
-        }
-        finishMotion = () => {
-          cancelAnimationFrame(frame);
-          draw(1);
-          exiting.forEach((node) => node.remove());
-          finishMotion = null;
-        };
-        const start = performance.now();
-        draw(0);
-        function tick(now) {
-          const progress = Math.min(1, (now - start) / 350);
-          draw(progress * progress * (3 - 2 * progress));
-          if (progress < 1) frame = requestAnimationFrame(tick);
-          else finishMotion();
-        }
-        frame = requestAnimationFrame(tick);
-      }
-
-      function restoreOverview() {
-        cy.elements().removeClass("focus-hidden named");
-        cy.nodes().not(":parent").not("[?isVariant]").forEach((node) => {
-          node.position(overviewPositions.get(node.id()));
-        });
-      }
-
-      function arrangeNeighborhood(nodes, edges) {
-        const neighbors = edges.connectedNodes().difference(nodes).not(":parent");
-        const focus = nodes.union(neighbors).union(edges).union(nodes.ancestors());
-        if (nodes.first().isParent()) {
-          relax(focus);
-        }
-        cy.elements().difference(focus).addClass("focus-hidden");
-        return focus;
-      }
-
-      function rebuildEdges() {
-        const edges = new Map();
-        data.edges.forEach((rule) => {
-          const from = data.nodes[rule.source];
-          const to = data.nodes[rule.target];
-          const source = expanded.has(from.name) ? variantId(from) : from.name;
-          const target = expanded.has(to.name) ? variantId(to) : to.name;
-          if (source === target) return;
-          const id = `edge:${source}:${target}`;
-          const edge = edges.get(id) || { id, source, target, count: 0 };
-          edge.count += 1;
-          edges.set(id, edge);
-        });
-        cy.edges().remove();
-        cy.add([...edges.values()].map((edge) => ({ data: edge })));
-      }
-
-      function toggleVariants(node) {
-        const family = families.get(node.id());
-        if (family.variants.length < 2) return;
-        const center = { ...node.position() };
-        if (expanded.has(node.id())) {
-          node.children().remove();
-          node.removeClass("expanded").removeStyle("font-size").position(center);
-          expanded.delete(node.id());
-        } else {
-          expanded.add(node.id());
-          node.addClass("expanded");
-          const columns = Math.ceil(Math.sqrt(family.variants.length));
-          const rows = Math.ceil(family.variants.length / columns);
-          cy.add(family.variants.map((variant, index) => ({
-            data: {
-              id: variantId(variant),
-              parent: node.id(),
-              isVariant: true,
-              label: Object.entries(variant.variant)
-                .map(([key, value]) => `${key}: ${value}`).join("\n"),
-              category: family.category,
-              rules: 0,
-            },
-            position: {
-              x: center.x + (index % columns - (columns - 1) / 2) * 175,
-              y: center.y + (Math.floor(index / columns) - (rows - 1) / 2) * 105,
-            },
-          })));
-        }
-        rebuildEdges();
-      }
-
-      const visibleElements = () =>
-        cy.elements().filter((element) => element.style("display") !== "none");
-
-      function sizeFocusLabels() {
-        const zoom = cy.zoom();
-        cy.startBatch();
-        cy.nodes().not(":parent").not("[?isVariant]")
-          .style("font-size", (node) => (node.hasClass("selected") ? 14 : 13) / zoom);
-        cy.nodes(".expanded").style("font-size", 18);
-        cy.endBatch();
-      }
-      let labelFrame;
-      function updateLabels() {
-        sizeFocusLabels();
-          cy.nodes().removeClass("named");
-          const reserved = cy.nodes("[?isVariant], :parent, .hovered, .selected")
-            .filter((node) => node.visible())
-            .map((node) => node.renderedBoundingBox({ includeNodes: false, includeLabels: true }));
-          const candidates = cy.nodes().not(":parent").not("[?isVariant]").not(".selected, .hovered")
-            .filter((node) => node.visible() && !node.hasClass("faded"))
-            .sort((a, b) => b.data("rules") - a.data("rules") || a.id().localeCompare(b.id()));
-          candidates.addClass("named");
-          const hidden = [];
-          candidates.forEach((node) => {
-              const box = node.renderedBoundingBox({ includeNodes: false, includeLabels: true });
-              const overlaps = reserved.some((other) => box.x1 < other.x2 + 8 &&
-                box.x2 > other.x1 - 8 && box.y1 < other.y2 + 5 && box.y2 > other.y1 - 5);
-              if (overlaps || box.x1 < 12 || box.x2 > cy.width() - 12 ||
-                box.y1 < 12 || box.y2 > cy.height() - 55) hidden.push(node);
-              else reserved.push(box);
-            });
-          cy.collection(hidden).removeClass("named");
-      }
-      cy.on("zoom pan", () => {
-        cancelAnimationFrame(labelFrame);
-        labelFrame = requestAnimationFrame(updateLabels);
-      });
-
-      function fit(focus = visibleElements(), maxZoom = 1) {
-        cy.resize();
-        cy.fit(focus, Math.max(32, Math.min(cy.width(), cy.height()) * 0.1));
-        cy.zoom(Math.min(cy.zoom(), maxZoom));
-        cy.center(focus);
-        cancelAnimationFrame(labelFrame);
-        updateLabels();
-      }
-
-      function applyScope() {
-        cy.nodes().removeClass("core-hidden");
-        if (scope === "core") cy.nodes("[?peripheral]").addClass("core-hidden");
-      }
-
-      function clearSelection() {
-        [...expanded].forEach((name) => toggleVariants(cy.getElementById(name)));
-        restoreOverview();
-        cy.elements().removeClass("selected neighbor faded search-match");
-        selectionType.textContent = "Details";
-        detail.replaceChildren();
-        applyScope();
-        fit();
-        selectedProblem = "";
-        selectedRules.clear();
-        renderBrowser();
-      }
-
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-
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-          ["family", "variant", "rule"].every((key) => button.dataset[key] === focused[key]))?.focus();
-      }
-
-      browserSearch.addEventListener("input", renderBrowser);
-      document.querySelectorAll("[data-browse]").forEach((button) =>
-        button.addEventListener("click", () => setBrowseMode(button.dataset.browse)));
-      browserList.addEventListener("click", (event) => {
-        const button = event.target.closest("button");
-        if (!button) return;
-        transition(() => {
-          if (button.dataset.family) selectNode(cy.getElementById(button.dataset.family));
-          else if (button.dataset.variant) selectNode(cy.getElementById(button.dataset.variant));
-          else {
-            const rule = data.edges[Number(button.dataset.rule)];
-            [...expanded].forEach((name) => toggleVariants(cy.getElementById(name)));
-            restoreOverview();
-            const source = data.nodes[rule.source], target = data.nodes[rule.target];
-            new Set([source.name, target.name]).forEach((name) => toggleVariants(cy.getElementById(name)));
-            const from = expanded.has(source.name) ? variantId(source) : source.name;
-            const to = expanded.has(target.name) ? variantId(target) : target.name;
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-            selectEdge(edge);
-          }
-        });
-      });
-
-      function applySearch() {
-        [...expanded].forEach((name) => toggleVariants(cy.getElementById(name)));
-        restoreOverview();
-        selectedProblem = "";
-        selectedRules.clear();
-        renderBrowser();
-        const query = search.value.trim().toLowerCase();
-        cy.elements().removeClass("selected neighbor faded search-match");
-        selectionType.textContent = "Details";
-        detail.replaceChildren();
-        applyScope();
-        if (!query) {
-          fit();
-          return;
-        }
-        const matches = cy.nodes().filter((node) => {
-          const schema = schemas.get(node.id());
-          return (
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-            [
-              node.id(),
-              displayName(node.id()),
-              schema?.description,
-              ...(schema?.aliases || []),
-            ]
-              .filter(Boolean)
-              .join(" ")
-              .toLowerCase()
-              .includes(query)
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-        });
-        cy.nodes().removeClass("core-hidden").addClass("faded");
-        cy.edges().addClass("faded");
-        matches.removeClass("faded").addClass("search-match");
-        matches.connectedEdges().removeClass("faded");
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-        if (matches.length) fit(matches.union(matches.connectedEdges()));
-      }
-
-      cy.on("tap", "node", (event) => transition(() => selectNode(event.target)));
-      cy.on("tap", "edge", (event) => transition(() => selectEdge(event.target)));
-      cy.on("tap", (event) => {
-        if (event.target === cy) transition(clearSelection);
-      });
-      cy.on("mouseover", "node", (event) => {
-        event.target.addClass("hovered");
-        event.target.connectedEdges().addClass("direction");
-        if (event.target.data("isVariant")) {
-          tooltip.textContent = `${displayName(event.target.parent().id())} · ${event.target.data("label")}`;
-          tooltip.style.display = "block";
-          return;
-        }
-        const family = families.get(event.target.id());
-        tooltip.textContent = `${displayName(family.name)} · ${family.variants.length} variant${family.variants.length === 1 ? "" : "s"} · ${family.rules} reductions`;
-        tooltip.style.display = "block";
-      });
-      cy.on("mouseover", "edge", (event) => {
-        event.target.addClass("hovered");
-        const edge = event.target;
-        tooltip.textContent = `${edge.source().data("label")} → ${edge.target().data("label")} · ${edge.data("count")} concrete rule${edge.data("count") === 1 ? "" : "s"}`;
-        tooltip.style.display = "block";
-      });
-      cy.on("mousemove", "node, edge", (event) => {
-        tooltip.style.left = `${event.originalEvent.clientX + 14}px`;
-        tooltip.style.top = `${event.originalEvent.clientY + 14}px`;
-      });
-      cy.on("mouseout", "node, edge", (event) => {
-        event.target.removeClass("hovered");
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-
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-        button.addEventListener("click", () => {
-          scope = button.dataset.scope;
-          document.querySelectorAll("[data-scope]").forEach((item) =>
-            item.setAttribute("aria-pressed", item === button),
-          );
-          search.value = "";
-          transition(clearSelection);
-        }),
-      );
-      document.querySelector("#reset-graph").addEventListener("click", () => {
-        search.value = "";
-        transition(clearSelection);
-      });
-      const workspace = document.querySelector(".graph-workspace");
-      const divider = document.querySelector(".graph-divider");
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-        divider.setAttribute("aria-valuemax", Math.round(maxPanelWidth()));
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-        canvasWidth = width;
-        canvasHeight = height;
-        describeDivider();
-        updateLabels();
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-      search.addEventListener("input", () => transition(applySearch));
-      search.addEventListener("keydown", (event) => {
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-        transition(() => {
-          applySearch();
-          const match = cy.nodes(".search-match").first();
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-
-      applyScope();
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-        search.disabled = false;
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-      document.querySelector(".graph-canvas-note").textContent = `Unable to load graph: ${error.message}`;
-      throw error;
-    }
-})();
diff --git a/docs/website/atlas-data.schema.json b/docs/website/atlas-data.schema.json
new file mode 100644
index 000000000..ea1e1eeb2
--- /dev/null
+++ b/docs/website/atlas-data.schema.json
@@ -0,0 +1,450 @@
+{
+  "$schema": "https://json-schema.org/draft/2020-12/schema",
+  "$id": "https://codingthrust.github.io/problem-reductions/contracts/atlas-data",
+  "title": "AtlasData",
+  "oneOf": [
+    {
+      "$ref": "#/$defs/AtlasSummary"
+    },
+    {
+      "$ref": "#/$defs/AtlasRecord"
+    }
+  ],
+  "$defs": {
+    "Name": {
+      "type": "string",
+      "pattern": "^[A-Za-z_][A-Za-z0-9_]*$"
+    },
+    "Category": {
+      "type": "string",
+      "enum": [
+        "graph",
+        "formula",
+        "set",
+        "algebraic",
+        "misc"
+      ]
+    },
+    "Variant": {
+      "type": "object",
+      "propertyNames": {
+        "minLength": 1
+      },
+      "additionalProperties": {
+        "type": "string",
+        "minLength": 1
+      }
+    },
+    "Index": {
+      "type": "integer",
+      "minimum": 0,
+      "maximum": 9007199254740991
+    },
+    "DocPath": {
+      "type": "string",
+      "pattern": "^(?:[A-Za-z0-9_-]+/)*[A-Za-z0-9_.-]+\\.html$"
+    },
+    "SourcePath": {
+      "type": "string",
+      "pattern": "^src/(?:[A-Za-z0-9_-]+/)*[A-Za-z0-9_-]+\\.rs$"
+    },
+    "MathML": {
+      "type": "string",
+      "pattern": "^<math xmlns=\"http://www\\.w3\\.org/1998/Math/MathML\" aria-label=\"[^\"<>]*\">(?:<(?:mrow|mi|mn|mo|mfrac|msup|msqrt)>|<mi mathvariant=\"normal\">|</(?:mrow|mi|mn|mo|mfrac|msup|msqrt)>|[^<>])*</math>$"
+    },
+    "SummaryNode": {
+      "type": "object",
+      "additionalProperties": false,
+      "required": [
+        "name",
+        "category",
+        "variant"
+      ],
+      "properties": {
+        "name": {
+          "$ref": "#/$defs/Name"
+        },
+        "category": {
+          "$ref": "#/$defs/Category"
+        },
+        "variant": {
+          "$ref": "#/$defs/Variant"
+        }
+      }
+    },
+    "SummaryEdge": {
+      "type": "object",
+      "additionalProperties": false,
+      "required": [
+        "source",
+        "target"
+      ],
+      "properties": {
+        "source": {
+          "$ref": "#/$defs/Index"
+        },
+        "target": {
+          "$ref": "#/$defs/Index"
+        }
+      }
+    },
+    "SummarySchema": {
+      "type": "object",
+      "additionalProperties": false,
+      "required": [
+        "name",
+        "description"
+      ],
+      "properties": {
+        "name": {
+          "$ref": "#/$defs/Name"
+        },
+        "description": {
+          "type": "string"
+        },
+        "display_name": {
+          "type": "string",
+          "minLength": 1
+        },
+        "aliases": {
+          "type": "array",
+          "items": {
+            "type": "string",
+            "minLength": 1
+          },
+          "uniqueItems": true
+        }
+      }
+    },
+    "RecordNode": {
+      "type": "object",
+      "additionalProperties": false,
+      "required": [
+        "name",
+        "category",
+        "variant",
+        "default",
+        "parameter_names",
+        "complexity",
+        "complexity_mathml",
+        "doc_path",
+        "api_path"
+      ],
+      "properties": {
+        "name": {
+          "$ref": "#/$defs/Name"
+        },
+        "category": {
+          "$ref": "#/$defs/Category"
+        },
+        "variant": {
+          "$ref": "#/$defs/Variant"
+        },
+        "default": {
+          "type": "boolean"
+        },
+        "parameter_names": {
+          "type": "array",
+          "items": {
+            "type": "string",
+            "minLength": 1
+          },
+          "uniqueItems": true
+        },
+        "complexity": {
+          "type": "string",
+          "minLength": 1
+        },
+        "complexity_mathml": {
+          "$ref": "#/$defs/MathML"
+        },
+        "doc_path": {
+          "$ref": "#/$defs/DocPath"
+        },
+        "api_path": {
+          "$ref": "#/$defs/DocPath"
+        }
+      }
+    },
+    "Parameter": {
+      "oneOf": [
+        {
+          "type": "object",
+          "additionalProperties": false,
+          "required": [
+            "field",
+            "contract",
+            "formula",
+            "reason",
+            "mathml"
+          ],
+          "properties": {
+            "field": {
+              "type": "string",
+              "minLength": 1
+            },
+            "contract": {
+              "type": "string",
+              "enum": [
+                "exact",
+                "upper_bound"
+              ]
+            },
+            "formula": {
+              "type": "string",
+              "minLength": 1
+            },
+            "reason": {
+              "type": "null"
+            },
+            "mathml": {
+              "$ref": "#/$defs/MathML"
+            }
+          }
+        },
+        {
+          "type": "object",
+          "additionalProperties": false,
+          "required": [
+            "field",
+            "contract",
+            "formula",
+            "reason",
+            "mathml"
+          ],
+          "properties": {
+            "field": {
+              "type": "string",
+              "minLength": 1
+            },
+            "contract": {
+              "type": "string",
+              "const": "unavailable"
+            },
+            "formula": {
+              "type": "null"
+            },
+            "reason": {
+              "type": "string",
+              "minLength": 1
+            },
+            "mathml": {
+              "type": "null"
+            }
+          }
+        }
+      ]
+    },
+    "RecordEdge": {
+      "type": "object",
+      "additionalProperties": false,
+      "required": [
+        "source",
+        "target",
+        "witness",
+        "aggregate",
+        "turing",
+        "parameter_contract_error",
+        "parameters",
+        "doc_path",
+        "source_path",
+        "api_path",
+        "test_path"
+      ],
+      "properties": {
+        "source": {
+          "$ref": "#/$defs/Index"
+        },
+        "target": {
+          "$ref": "#/$defs/Index"
+        },
+        "witness": {
+          "type": "boolean"
+        },
+        "aggregate": {
+          "type": "boolean"
+        },
+        "turing": {
+          "type": "boolean"
+        },
+        "parameter_contract_error": {
+          "type": [
+            "string",
+            "null"
+          ],
+          "minLength": 1
+        },
+        "parameters": {
+          "type": "array",
+          "items": {
+            "$ref": "#/$defs/Parameter"
+          }
+        },
+        "doc_path": {
+          "$ref": "#/$defs/DocPath"
+        },
+        "source_path": {
+          "$ref": "#/$defs/SourcePath"
+        },
+        "api_path": {
+          "$ref": "#/$defs/DocPath"
+        },
+        "test_path": {
+          "anyOf": [
+            {
+              "$ref": "#/$defs/SourcePath"
+            },
+            {
+              "type": "null"
+            }
+          ]
+        }
+      }
+    },
+    "Field": {
+      "type": "object",
+      "additionalProperties": false,
+      "required": [
+        "name",
+        "type_name",
+        "description"
+      ],
+      "properties": {
+        "name": {
+          "type": "string",
+          "minLength": 1
+        },
+        "type_name": {
+          "type": "string",
+          "minLength": 1
+        },
+        "description": {
+          "type": "string"
+        }
+      }
+    },
+    "RecordSchema": {
+      "type": "object",
+      "additionalProperties": false,
+      "required": [
+        "name",
+        "description",
+        "category",
+        "fields",
+        "module_path",
+        "source_path"
+      ],
+      "properties": {
+        "name": {
+          "$ref": "#/$defs/Name"
+        },
+        "description": {
+          "type": "string"
+        },
+        "display_name": {
+          "type": "string",
+          "minLength": 1
+        },
+        "aliases": {
+          "type": "array",
+          "items": {
+            "type": "string",
+            "minLength": 1
+          },
+          "uniqueItems": true
+        },
+        "category": {
+          "$ref": "#/$defs/Category"
+        },
+        "fields": {
+          "type": "array",
+          "items": {
+            "$ref": "#/$defs/Field"
+          }
+        },
+        "module_path": {
+          "type": "string",
+          "minLength": 1
+        },
+        "source_path": {
+          "$ref": "#/$defs/SourcePath"
+        }
+      }
+    },
+    "AtlasSummary": {
+      "type": "object",
+      "additionalProperties": false,
+      "required": [
+        "kind",
+        "nodes",
+        "edges",
+        "schemas"
+      ],
+      "properties": {
+        "kind": {
+          "type": "string",
+          "const": "summary"
+        },
+        "nodes": {
+          "type": "array",
+          "items": {
+            "$ref": "#/$defs/SummaryNode"
+          },
+          "minItems": 1
+        },
+        "edges": {
+          "type": "array",
+          "items": {
+            "$ref": "#/$defs/SummaryEdge"
+          }
+        },
+        "schemas": {
+          "type": "array",
+          "items": {
+            "$ref": "#/$defs/SummarySchema"
+          },
+          "minItems": 1
+        }
+      },
+      "title": "AtlasSummary"
+    },
+    "AtlasRecord": {
+      "type": "object",
+      "additionalProperties": false,
+      "required": [
+        "kind",
+        "nodes",
+        "edges",
+        "schemas"
+      ],
+      "properties": {
+        "kind": {
+          "type": "string",
+          "const": "record"
+        },
+        "nodes": {
+          "type": "array",
+          "items": {
+            "$ref": "#/$defs/RecordNode"
+          },
+          "minItems": 1
+        },
+        "edges": {
+          "type": "array",
+          "items": {
+            "$ref": "#/$defs/RecordEdge"
+          }
+        },
+        "schemas": {
+          "type": "array",
+          "items": {
+            "$ref": "#/$defs/RecordSchema"
+          },
+          "minItems": 1,
+          "maxItems": 1
+        }
+      },
+      "title": "AtlasRecord"
+    }
+  }
+}
diff --git a/docs/website/cli-preview.png b/docs/website/cli-preview.png
deleted file mode 100644
index e15c6aee3..000000000
Binary files a/docs/website/cli-preview.png and /dev/null differ
diff --git a/docs/website/docs-preview.png b/docs/website/docs-preview.png
deleted file mode 100644
index 3183768bb..000000000
Binary files a/docs/website/docs-preview.png and /dev/null differ
diff --git a/docs/website/graph-details.schema.json b/docs/website/graph-details.schema.json
new file mode 100644
index 000000000..8e0b8bcf4
--- /dev/null
+++ b/docs/website/graph-details.schema.json
@@ -0,0 +1,16 @@
+{
+  "$schema": "https://json-schema.org/draft/2020-12/schema",
+  "$id": "https://codingthrust.github.io/problem-reductions/contracts/graph-details",
+  "title": "GraphDetailsIndex",
+  "type": "object",
+  "additionalProperties": false,
+  "required": ["entries", "anchors"],
+  "properties": {
+    "entries": {
+      "type": "object", "minProperties": 1,
+      "propertyNames": {"pattern": "^(problem:.+|rule:.+|references|footnotes)$"},
+      "additionalProperties": {"type": "string", "minLength": 1}
+    },
+    "anchors": {"type": "object", "additionalProperties": {"type": "string", "minLength": 1}}
+  }
+}
diff --git a/docs/website/graph-scene.schema.json b/docs/website/graph-scene.schema.json
new file mode 100644
index 000000000..7510f608a
--- /dev/null
+++ b/docs/website/graph-scene.schema.json
@@ -0,0 +1,48 @@
+{
+  "$schema": "https://json-schema.org/draft/2020-12/schema",
+  "$id": "https://codingthrust.github.io/problem-reductions/contracts/graph-scene",
+  "title": "GraphSceneData",
+  "type": "object",
+  "additionalProperties": false,
+  "required": ["nodes", "edges", "aliases", "layout"],
+  "properties": {
+    "nodes": {
+      "type": "array", "minItems": 1,
+      "items": {
+        "type": "object", "additionalProperties": false,
+        "required": ["name", "category", "variant", "default"],
+        "properties": {
+          "name": {"type": "string", "minLength": 1},
+          "category": {"enum": ["graph", "formula", "set", "algebraic", "misc"], "type": "string"},
+          "variant": {"type": "object", "additionalProperties": {"type": "string", "minLength": 1}},
+          "default": {"type": "boolean"}
+        }
+      }
+    },
+    "edges": {
+      "type": "array",
+      "items": {
+        "type": "object", "additionalProperties": false,
+        "required": ["source", "target", "witness", "turing"],
+        "properties": {
+          "source": {"type": "integer", "minimum": 0, "maximum": 9007199254740991},
+          "target": {"type": "integer", "minimum": 0, "maximum": 9007199254740991},
+          "witness": {"type": "boolean"},
+          "turing": {"type": "boolean"}
+        }
+      }
+    },
+    "aliases": {
+      "type": "object",
+      "additionalProperties": {"type": "array", "items": {"type": "string", "minLength": 1}, "uniqueItems": true}
+    },
+    "layout": {
+      "type": "object",
+      "additionalProperties": {
+        "type": "object", "additionalProperties": false,
+        "required": ["x", "y"],
+        "properties": {"x": {"type": "number"}, "y": {"type": "number"}}
+      }
+    }
+  }
+}
diff --git a/docs/website/graph.html b/docs/website/graph.html
index d01afbbde..dcb029482 100644
--- a/docs/website/graph.html
+++ b/docs/website/graph.html
@@ -1,127 +1,69 @@
 <!doctype html>
 <html lang="en">
-  <head>
-    <meta charset="utf-8" />
-    <meta name="viewport" content="width=device-width, initial-scale=1" />
-    <meta name="theme-color" content="#101713" />
-    <meta name="color-scheme" content="dark" />
-    <meta
-      name="description"
-      content="Explore the executable graph of NP-hard problems and reductions."
-    />
-    <title>Reduction Graph — Problem Reductions</title>
-    <link rel="icon" href="./assets/favicon.svg" type="image/svg+xml" />
-    <link rel="stylesheet" href="./assets/site.css" />
-    <link rel="stylesheet" href="./assets/graph.css" />
-    <link rel="stylesheet" href="./assets/details.css" />
-    <script src="./assets/cytoscape.min.js" defer></script>
-    <script src="./assets/graph-layout.js" defer></script>
-    <script src="./assets/graph-data.js" defer></script>
-    <script src="./assets/details.js" defer></script>
-    <script src="./assets/graph.js" defer></script>
-  </head>
-  <body class="graph-page">
-    <a class="skip-link" href="#reduction-graph">Skip to graph</a>
-    <header class="site-header">
-      <div class="header-inner graph-header">
-        <a class="wordmark" href="./" aria-label="Problem Reductions home"
-          ><img
-            class="project-logo"
-            src="./assets/logo.svg"
-            alt="100 Problem-Reductions"
-            width="372"
-            height="107"
-        /></a>
-        <label class="graph-search">
-          <svg
-            width="18"
-            height="18"
-            viewBox="0 0 24 24"
-            fill="none"
-            stroke="currentColor"
-            stroke-width="1.5"
-            aria-hidden="true"
-          >
-            <circle cx="10" cy="10" r="6"></circle>
-            <path d="m15 15 5 5"></path>
-          </svg>
-          <input
-            id="graph-search"
-            type="search"
-            placeholder="Search the reduction graph…"
-            aria-label="Search the reduction graph"
-            autocomplete="off"
-          />
-          <kbd>/</kbd>
-        </label>
-        <nav aria-label="Main navigation">
-          <a href="./">Home</a>
-          <a href="./graph.html" aria-current="page">Graph</a>
-          <a href="./#atlas">Atlas</a>
-          <a href="./introduction.html" class="docs-nav"
-            >Docs <span aria-hidden="true">↗</span></a
-          >
-          <a href="./open-questions/"
-            >Open questions <span aria-hidden="true">↗</span></a
-          >
-        </nav>
-      </div>
-    </header>
+<head>
+  <meta charset="utf-8">
+  <meta name="viewport" content="width=device-width, initial-scale=1, viewport-fit=cover">
+  <meta name="theme-color" content="#0b110d">
+  <meta name="color-scheme" content="dark">
+  <title>Reduction Paths — Problem Reductions</title>
+  <link rel="icon" href="./assets/favicon.svg" type="image/svg+xml">
+  <link rel="preload" href="./assets/graph-scene.json.gz" as="fetch" type="application/gzip" crossorigin>
+  <link rel="preload" href="./assets/path-graph.json.gz" as="fetch" type="application/gzip" crossorigin>
+  <link rel="preload" href="./assets/path-selection_bg.wasm.gz" as="fetch" type="application/gzip" crossorigin>
+  <link rel="preload" href="./assets/fonts/dm-sans-variable.woff2" as="font" type="font/woff2" crossorigin>
+  <link rel="stylesheet" href="./src/styles/site.css">
+  <link rel="stylesheet" href="./src/styles/details.css">
+  <link rel="stylesheet" href="./src/styles/graph.css">
+  <script type="module" src="./src/pages/graph-startup.ts"></script>
+  <script type="module" src="./src/pages/graph.ts"></script>
+</head>
+<body data-scene="./assets/graph-scene.json.gz">
+<header class="site-header">
+  <div class="header-inner">
+    <a class="wordmark" href="./index.html#home" aria-label="Problem Reductions home"><img class="project-logo" src="./assets/logo.svg" alt="100 Problem-Reductions" width="372" height="107"></a>
+    <nav aria-label="Main navigation">
+      <a href="./index.html#home">Home</a>
+      <a href="./graph.html" aria-current="page">Graph</a>
+      <a href="./index.html#atlas">Atlas</a>
+      <a href="./index.html#infrastructure">Get started</a>
+      <a href="./introduction.html" class="docs-nav">Docs <i class="arrow ne" aria-hidden="true"></i></a>
+      <a href="./open-questions/">Open questions <i class="arrow ne" aria-hidden="true"></i></a>
+    </nav>
+  </div>
+</header>
+<main id="canvas" aria-label="Reduction graph"><div id="cy"></div></main>
 
-    <main id="reduction-graph" tabindex="-1">
-      <div class="graph-toolbar">
-        <div>
-          <strong>Reduction graph</strong>
-          <span
-            >__PROBLEM_COUNT__ families · __VARIANT_COUNT__ variants ·
-            __RULE_COUNT__ directed reductions</span
-          >
-        </div>
-        <div class="graph-view-controls" aria-label="Graph view">
-          <button data-scope="core" aria-pressed="true">Connected core</button>
-          <button data-scope="all" aria-pressed="false">All problems</button>
-          <button id="reset-graph">Reset view</button>
-        </div>
-      </div>
+<section class="panel" aria-label="Reduction paths">
+  <header class="panel-head"><h1 class="brand"><a href="./index.html">Reduction paths</a></h1></header>
+  <div class="ends" id="ends">
+    <div class="end from">
+      <span class="pin" aria-hidden="true"></span>
+      <div><input id="source" placeholder="Start problem" autocomplete="off" spellcheck="false" aria-label="Start problem" role="combobox" aria-autocomplete="list" aria-expanded="false" aria-controls="suggest"><div class="options" id="source-options" hidden></div></div>
+    </div>
+    <div class="end to">
+      <span class="pin" aria-hidden="true"></span>
+      <div><input id="target" placeholder="End problem" autocomplete="off" spellcheck="false" aria-label="End problem" role="combobox" aria-autocomplete="list" aria-expanded="false" aria-controls="suggest"><div class="options" id="target-options" hidden></div></div>
+    </div>
+    <button class="swap" id="swap" aria-label="Swap start and end"><svg width="16" height="16" viewBox="0 0 16 16" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round"><path d="M5 2.5v11M2.5 5 5 2.5 7.5 5M11 13.5v-11M8.5 11l2.5 2.5 2.5-2.5"/></svg></button>
+    <div class="suggest" id="suggest" role="listbox" aria-label="Problems" hidden></div>
+  </div>
+  <div id="search-status" class="sr-only" role="status"></div>
+  <div class="results" id="results" aria-live="polite"></div>
+</section>
 
-      <div class="graph-workspace" inert>
-        <aside class="graph-browser" aria-label="Graph browser">
-          <div class="browser-modes" aria-label="Browse mode">
-            <button data-browse="problems" aria-pressed="true">Problems</button>
-            <button data-browse="rules" aria-pressed="false">Rules</button>
-          </div>
-          <input id="browser-search" type="search" placeholder="Search problems…" aria-label="Search graph list" />
-          <p id="browser-count" aria-live="polite"></p>
-          <div id="browser-list" aria-label="Problems and rules"></div>
-        </aside>
-        <section class="graph-canvas" aria-label="Interactive reduction graph">
-            <div id="cy" aria-busy="true"></div>
-          <div class="graph-legend" aria-label="Problem categories">
-            <span><i class="category-graph"></i>Graph</span>
-            <span><i class="category-formula"></i>Formula</span>
-            <span><i class="category-set"></i>Set</span>
-            <span><i class="category-algebraic"></i>Algebraic</span>
-            <span><i class="category-misc"></i>Misc</span>
-          </div>
-          <p class="graph-canvas-note">
-            Hover a node or connection to see reduction direction.
-          </p>
-        </section>
+<div class="pop" id="pop" role="dialog" aria-labelledby="pop-title" hidden></div>
+<nav class="dock" aria-label="Graph navigation">
+  <button id="zoom-in" aria-label="Zoom in"><svg width="14" height="14" viewBox="0 0 14 14" stroke="currentColor" stroke-width="1.5" stroke-linecap="round"><path d="M7 2v10M2 7h10"/></svg></button>
+  <button id="zoom-out" aria-label="Zoom out"><svg width="14" height="14" viewBox="0 0 14 14" stroke="currentColor" stroke-width="1.5" stroke-linecap="round"><path d="M2 7h10"/></svg></button>
+  <button id="fit" aria-label="Show whole graph"><svg width="14" height="14" viewBox="0 0 14 14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round"><path d="M1.5 5V1.5H5M9 1.5h3.5V5M12.5 9v3.5H9M5 12.5H1.5V9"/></svg></button>
+</nav>
 
-        <div class="graph-divider" role="separator" tabindex="0"
-          aria-label="Resize details panel" aria-orientation="vertical"
-          aria-controls="graph-inspector" aria-valuemin="240" aria-valuenow="320"></div>
-        <aside id="graph-inspector" class="graph-inspector" aria-label="Selection details">
-          <div class="inspector-heading">
-            <span id="selection-type">Details</span>
-          </div>
-          <div id="graph-detail" class="graph-detail"></div>
-        </aside>
-      </div>
-    </main>
-    <div class="graph-tooltip" id="graph-tooltip" role="tooltip"></div>
-    <noscript>
-      <p class="wrap">The interactive reduction graph requires JavaScript.</p>
-    </noscript>
-  </body>
+<div id="details-drawer" role="dialog" aria-labelledby="details-title" hidden>
+  <div class="drawer-head">
+    <div><h2 id="details-title"></h2><a id="drawer-atlas">Open in Atlas <i class="arrow ne" aria-hidden="true"></i></a></div>
+    <button id="close-details" type="button" aria-label="Close details">×</button>
+  </div>
+  <div id="drawer-body" class="graph-detail"></div>
+</div>
+</body>
 </html>
diff --git a/docs/website/index.html b/docs/website/index.html
index 6669490a1..bab78e270 100644
--- a/docs/website/index.html
+++ b/docs/website/index.html
@@ -19,16 +19,15 @@
     <link rel="icon" href="./assets/favicon.svg" type="image/svg+xml" />
     <link
       rel="preload"
-      href="./assets/fonts/dm-sans-regular.ttf"
+      href="./assets/fonts/dm-sans-variable.woff2"
       as="font"
-      type="font/ttf"
+      type="font/woff2"
       crossorigin
     />
-    <link rel="stylesheet" href="./assets/site.css" />
-    <link rel="stylesheet" href="./assets/details.css" />
-    <script src="./assets/home-data.js" defer></script>
-    <script src="./assets/details.js" defer></script>
-    <script src="./assets/site.js" defer></script>
+    <link rel="stylesheet" href="./src/styles/site.css" />
+    <link rel="stylesheet" href="./src/styles/details.css" />
+    <script type="module" src="./assets/home-data.js"></script>
+    <script type="module" src="./src/pages/site.ts"></script>
   </head>
   <body>
     <a class="skip-link" href="#main">Skip to content</a>
@@ -48,10 +47,10 @@
           <a href="#atlas" data-nav="atlas">Atlas</a>
           <a href="#infrastructure" data-nav="infrastructure">Get started</a>
           <a href="./introduction.html" class="docs-nav"
-            >Docs <span aria-hidden="true">↗</span></a
+            >Docs <i class="arrow ne" aria-hidden="true"></i></a
           >
           <a href="./open-questions/"
-            >Open questions <span aria-hidden="true">↗</span></a
+            >Open questions <i class="arrow ne" aria-hidden="true"></i></a
           >
         </nav>
       </div>
@@ -66,9 +65,9 @@ <h1>Problem<br />Reductions</h1>
           </p>
           <div class="hero-actions">
             <a class="button primary" href="./graph.html"
-              >Explore the graph <span aria-hidden="true">↗</span></a
-            ><a class="text-link" href="#research"
-              >Research loop <span aria-hidden="true">→</span></a
+              >Explore the graph <i class="arrow ne" aria-hidden="true"></i></a
+            ><a class="text-link" href="#infrastructure"
+              >Get started <i class="arrow e" aria-hidden="true"></i></a
             >
           </div>
         </div>
@@ -92,9 +91,45 @@ <h1>Problem<br />Reductions</h1>
         </div>
         <a href="./reductions.pdf"
           >Theory, constructions<br />&amp; proofs
-          <span aria-hidden="true">↗</span></a
+          <i class="arrow ne" aria-hidden="true"></i></a
         >
       </section>
+      <section class="infrastructure-section wrap" id="infrastructure">
+        <div>
+          <h2>Get started</h2>
+          <p>
+            Use the atlas from the terminal, from Rust, or through an
+            agent.<br />All three share the same models and constructions.
+          </p>
+          <div class="hero-actions">
+            <a class="button primary" href="./introduction.html"
+              >Read the documentation <i class="arrow ne" aria-hidden="true"></i></a
+            ><a class="text-link" href="./cli.html#terminal-session"
+              >Watch the CLI <i class="arrow ne" aria-hidden="true"></i></a
+            >
+          </div>
+        </div>
+        <div class="terminal">
+          <div class="terminal-header">
+            <span><i></i><i></i><i></i></span
+            ><button
+              class="copy-button"
+              data-copy="cargo install problemreductions-cli"
+              aria-label="Copy installation command"
+            >
+              Copy
+            </button>
+          </div>
+          <pre><span class="terminal-comment"># Install the CLI</span>
+<span class="terminal-prompt">$</span> cargo install problemreductions-cli
+
+<span class="terminal-comment"># Explore a problem</span>
+<span class="terminal-prompt">$</span> pred show MIS
+
+<span class="terminal-comment"># Search for a route to a solver</span>
+<span class="terminal-prompt">$</span> pred path MIS ILP</pre>
+        </div>
+      </section>
       <section class="section wrap" id="connections">
         <div class="section-heading">
           <div>
@@ -109,10 +144,36 @@ <h2>Problems and reductions</h2>
         <div class="problem-showcase" id="problem-showcase"></div>
         <div class="section-bottom">
           <a class="text-link" href="#atlas"
-            >Browse all problems <span aria-hidden="true">→</span></a
+            >Browse all problems <i class="arrow e" aria-hidden="true"></i></a
           >
         </div>
       </section>
+      <section class="section wrap evidence-section" id="featured">
+        <div class="section-heading">
+          <div>
+            <h2>Example reduction</h2>
+          </div>
+          <p>
+            Every registered reduction has a statement and proof in the paper
+            and executable code with solution recovery.
+          </p>
+        </div>
+        <a class="featured-result" id="featured-result-link" href="#atlas"
+          ><div class="featured-copy">
+            <h3>Vertex Cover to<br />Independent Set</h3>
+            <p>
+              Remove a vertex cover and what remains is an independent set:
+              no edge can join two vertices outside the cover. A solver for
+              one problem therefore solves the other, and the answer maps back
+              by taking the complement.
+            </p>
+            <span class="text-link"
+              >Examine the reduction <i class="arrow ne" aria-hidden="true"></i></span
+            >
+          </div>
+          <div class="complement-art" id="featured-art"></div
+        ></a>
+      </section>
       <section class="research-section" id="research">
         <div class="wrap">
           <div class="section-heading">
@@ -165,72 +226,11 @@ <h3>Grow the atlas</h3>
               question selection and persistent experiment records.
             </p>
             <a href="./skills.html"
-              >Explore agent workflows <span aria-hidden="true">↗</span></a
+              >Explore agent workflows <i class="arrow ne" aria-hidden="true"></i></a
             >
           </div>
         </div>
       </section>
-      <section class="section wrap evidence-section" id="featured">
-        <div class="section-heading">
-          <div>
-            <h2>Example reduction</h2>
-          </div>
-          <p>
-            Every registered reduction has a statement and proof in the paper
-            and executable code with solution recovery.
-          </p>
-        </div>
-        <a class="featured-result" id="featured-result-link" href="#atlas"
-          ><div class="featured-copy">
-            <h3>Vertex Cover to<br />Independent Set</h3>
-            <p>
-              A vertex cover and an independent set are complements. A simple
-              construction shows how the atlas connects definitions, solution
-              recovery, and executable code.
-            </p>
-            <span class="text-link"
-              >Examine the reduction <span aria-hidden="true">↗</span></span
-            >
-          </div>
-          <div class="complement-art" id="featured-art"></div
-        ></a>
-      </section>
-      <section class="infrastructure-section wrap" id="infrastructure">
-        <div>
-          <h2>Get started</h2>
-          <p>
-            Use the atlas from the terminal, from Rust, or through an
-            agent.<br />All three share the same models and constructions.
-          </p>
-          <div class="hero-actions">
-            <a class="button primary" href="./introduction.html"
-              >Read the documentation <span aria-hidden="true">↗</span></a
-            ><a class="text-link" href="./cli.html#terminal-session"
-              >Watch the CLI <span aria-hidden="true">↗</span></a
-            >
-          </div>
-        </div>
-        <div class="terminal">
-          <div class="terminal-header">
-            <span><i></i><i></i><i></i></span
-            ><button
-              class="copy-button"
-              data-copy="cargo install problemreductions-cli"
-              aria-label="Copy installation command"
-            >
-              Copy
-            </button>
-          </div>
-          <pre><span class="terminal-comment"># Install the CLI</span>
-<span class="terminal-prompt">$</span> cargo install problemreductions-cli
-
-<span class="terminal-comment"># Explore a problem</span>
-<span class="terminal-prompt">$</span> pred show MIS
-
-<span class="terminal-comment"># Search for a route to a solver</span>
-<span class="terminal-prompt">$</span> pred path MIS ILP</pre>
-        </div>
-      </section>
     </main>
     <footer class="site-footer wrap">
       <div>
@@ -245,10 +245,10 @@ <h2>Get started</h2>
       </div>
       <div>
         <a href="https://github.com/CodingThrust/problem-reductions"
-          >GitHub ↗</a
+          >GitHub <i class="arrow ne" aria-hidden="true"></i></a
         >
-        <a href="./reductions.pdf">Paper ↗</a>
-        <a href="./introduction.html">Documentation ↗</a>
+        <a href="./reductions.pdf">Paper <i class="arrow ne" aria-hidden="true"></i></a>
+        <a href="./introduction.html">Documentation <i class="arrow ne" aria-hidden="true"></i></a>
         <span>Open source · MIT</span>
       </div>
     </footer>
diff --git a/docs/website/native-exports.schema.json b/docs/website/native-exports.schema.json
new file mode 100644
index 000000000..32c42e8b6
--- /dev/null
+++ b/docs/website/native-exports.schema.json
@@ -0,0 +1,293 @@
+{
+  "$schema": "https://json-schema.org/draft/2020-12/schema",
+  "$id": "https://codingthrust.github.io/problem-reductions/contracts/native-exports",
+  "title": "NativeExports",
+  "type": "object",
+  "additionalProperties": false,
+  "required": [
+    "graph",
+    "schemas"
+  ],
+  "properties": {
+    "graph": {
+      "type": "object",
+      "additionalProperties": false,
+      "required": [
+        "nodes",
+        "edges",
+        "aliases"
+      ],
+      "properties": {
+        "nodes": {
+          "type": "array",
+          "minItems": 1,
+          "items": {
+            "type": "object",
+            "additionalProperties": false,
+            "required": [
+              "name",
+              "variant",
+              "default",
+              "parameter_names",
+              "category",
+              "doc_path",
+              "complexity"
+            ],
+            "properties": {
+              "name": {
+                "$ref": "#/$defs/Name"
+              },
+              "variant": {
+                "type": "object",
+                "propertyNames": {
+                  "minLength": 1
+                },
+                "additionalProperties": {
+                  "type": "string",
+                  "minLength": 1
+                }
+              },
+              "default": {
+                "type": "boolean"
+              },
+              "parameter_names": {
+                "type": "array",
+                "uniqueItems": true,
+                "items": {
+                  "type": "string",
+                  "minLength": 1
+                }
+              },
+              "category": {
+                "$ref": "#/$defs/Category"
+              },
+              "doc_path": {
+                "$ref": "#/$defs/DocPath"
+              },
+              "complexity": {
+                "type": "string",
+                "minLength": 1
+              }
+            }
+          }
+        },
+        "edges": {
+          "type": "array",
+          "items": {
+            "type": "object",
+            "additionalProperties": false,
+            "required": [
+              "source",
+              "target",
+              "witness",
+              "turing",
+              "parameter_contract_error",
+              "parameters",
+              "aggregate",
+              "doc_path"
+            ],
+            "properties": {
+              "source": {
+                "type": "integer",
+                "minimum": 0,
+                "maximum": 9007199254740991
+              },
+              "target": {
+                "type": "integer",
+                "minimum": 0,
+                "maximum": 9007199254740991
+              },
+              "witness": {
+                "type": "boolean"
+              },
+              "turing": {
+                "type": "boolean"
+              },
+              "parameter_contract_error": {
+                "type": [
+                  "string",
+                  "null"
+                ],
+                "minLength": 1
+              },
+              "parameters": {
+                "type": "array",
+                "items": {
+                  "$ref": "#/$defs/Parameter"
+                }
+              },
+              "aggregate": {
+                "type": "boolean"
+              },
+              "doc_path": {
+                "$ref": "#/$defs/DocPath"
+              }
+            }
+          }
+        },
+        "aliases": {
+          "type": "object",
+          "additionalProperties": {
+            "type": "array",
+            "items": {
+              "type": "string",
+              "minLength": 1
+            },
+            "uniqueItems": true
+          }
+        }
+      }
+    },
+    "schemas": {
+      "type": "array",
+      "minItems": 1,
+      "items": {
+        "type": "object",
+        "additionalProperties": false,
+        "required": [
+          "name",
+          "description",
+          "category",
+          "fields",
+          "module_path"
+        ],
+        "properties": {
+          "name": {
+            "$ref": "#/$defs/Name"
+          },
+          "description": {
+            "type": "string"
+          },
+          "display_name": {
+            "type": "string",
+            "minLength": 1
+          },
+          "aliases": {
+            "type": "array",
+            "items": {
+              "type": "string",
+              "minLength": 1
+            },
+            "uniqueItems": true
+          },
+          "category": {
+            "$ref": "#/$defs/Category"
+          },
+          "fields": {
+            "type": "array",
+            "items": {
+              "$ref": "#/$defs/Field"
+            }
+          },
+          "module_path": {
+            "type": "string",
+            "minLength": 1
+          }
+        }
+      }
+    }
+  },
+  "$defs": {
+    "Name": {
+      "type": "string",
+      "pattern": "^[A-Za-z_][A-Za-z0-9_]*$"
+    },
+    "Category": {
+      "type": "string",
+      "enum": [
+        "graph",
+        "formula",
+        "set",
+        "algebraic",
+        "misc"
+      ]
+    },
+    "Field": {
+      "type": "object",
+      "additionalProperties": false,
+      "required": [
+        "name",
+        "type_name",
+        "description"
+      ],
+      "properties": {
+        "name": {
+          "type": "string",
+          "minLength": 1
+        },
+        "type_name": {
+          "type": "string",
+          "minLength": 1
+        },
+        "description": {
+          "type": "string"
+        }
+      }
+    },
+    "DocPath": {
+      "type": "string",
+      "pattern": "^(?:[A-Za-z0-9_-]+/)*[A-Za-z0-9_.-]+\\.html$"
+    },
+    "Parameter": {
+      "oneOf": [
+        {
+          "type": "object",
+          "additionalProperties": false,
+          "required": [
+            "field",
+            "contract",
+            "formula",
+            "reason"
+          ],
+          "properties": {
+            "field": {
+              "type": "string",
+              "minLength": 1
+            },
+            "contract": {
+              "type": "string",
+              "enum": [
+                "exact",
+                "upper_bound"
+              ]
+            },
+            "formula": {
+              "type": "string",
+              "minLength": 1
+            },
+            "reason": {
+              "type": "null"
+            }
+          }
+        },
+        {
+          "type": "object",
+          "additionalProperties": false,
+          "required": [
+            "field",
+            "contract",
+            "formula",
+            "reason"
+          ],
+          "properties": {
+            "field": {
+              "type": "string",
+              "minLength": 1
+            },
+            "contract": {
+              "type": "string",
+              "const": "unavailable"
+            },
+            "formula": {
+              "type": "null"
+            },
+            "reason": {
+              "type": "string",
+              "minLength": 1
+            }
+          }
+        }
+      ]
+    }
+  }
+}
diff --git a/docs/website/path-graph.schema.json b/docs/website/path-graph.schema.json
new file mode 100644
index 000000000..2b170708d
--- /dev/null
+++ b/docs/website/path-graph.schema.json
@@ -0,0 +1,67 @@
+{
+  "$schema": "https://json-schema.org/draft/2020-12/schema",
+  "$id": "https://codingthrust.github.io/problem-reductions/contracts/path-graph",
+  "title": "PathGraphData",
+  "type": "object",
+  "additionalProperties": false,
+  "required": ["nodes", "edges"],
+  "properties": {
+    "nodes": {
+      "type": "array", "minItems": 1,
+      "items": {
+        "type": "object", "additionalProperties": false,
+        "required": ["name", "variant", "default", "parameter_names"],
+        "properties": {
+          "name": {"type": "string", "minLength": 1},
+          "variant": {
+            "type": "object", "propertyNames": {"minLength": 1},
+            "additionalProperties": {"type": "string", "minLength": 1}
+          },
+          "default": {"type": "boolean"},
+          "parameter_names": {"type": "array", "uniqueItems": true, "items": {"type": "string", "minLength": 1}}
+        }
+      }
+    },
+    "edges": {
+      "type": "array",
+      "items": {
+        "type": "object", "additionalProperties": false,
+        "required": ["source", "target", "witness", "turing", "parameters", "parameter_contract_error"],
+        "properties": {
+          "source": {"type": "integer", "minimum": 0, "maximum": 9007199254740991},
+          "target": {"type": "integer", "minimum": 0, "maximum": 9007199254740991},
+          "witness": {"type": "boolean"},
+          "turing": {"type": "boolean"},
+          "parameter_contract_error": {"type": ["string", "null"], "minLength": 1},
+          "parameters": {"type": "array", "items": {"$ref": "#/$defs/Parameter"}}
+        }
+      }
+    }
+  },
+  "$defs": {
+    "Parameter": {
+      "oneOf": [
+        {
+          "type": "object", "additionalProperties": false,
+          "required": ["field", "contract", "formula", "reason"],
+          "properties": {
+            "field": {"type": "string", "minLength": 1},
+            "contract": {"type": "string", "enum": ["exact", "upper_bound"]},
+            "formula": {"type": "string", "minLength": 1},
+            "reason": {"type": "null"}
+          }
+        },
+        {
+          "type": "object", "additionalProperties": false,
+          "required": ["field", "contract", "formula", "reason"],
+          "properties": {
+            "field": {"type": "string", "minLength": 1},
+            "contract": {"type": "string", "const": "unavailable"},
+            "formula": {"type": "null"},
+            "reason": {"type": "string", "minLength": 1}
+          }
+        }
+      ]
+    }
+  }
+}
diff --git a/docs/website/preview.png b/docs/website/preview.png
deleted file mode 100644
index 362c90a3a..000000000
Binary files a/docs/website/preview.png and /dev/null differ
diff --git a/docs/website/src/lib/graph-details-data.mts b/docs/website/src/lib/graph-details-data.mts
new file mode 100644
index 000000000..3f71f95cf
--- /dev/null
+++ b/docs/website/src/lib/graph-details-data.mts
@@ -0,0 +1,12 @@
+export function validateDetailURL(entry: string, page: URL, articles: URL): void {
+  const error = () => new Error('Invalid documentation index. Reload the current release.');
+  let url: URL;
+  let path: string;
+  try {
+    url = new URL(entry, page);
+    path = decodeURIComponent(url.pathname);
+  } catch { throw error(); }
+  if (url.protocol !== page.protocol || url.origin !== page.origin || url.username || url.password || url.search || url.hash
+      || !path.startsWith(decodeURIComponent(articles.pathname)) || !path.endsWith('.html')
+      || path.includes('\\') || path.split('/').some(part => part === '.' || part === '..')) throw error();
+}
diff --git a/docs/website/src/lib/graph-growth.mts b/docs/website/src/lib/graph-growth.mts
new file mode 100644
index 000000000..b4294dc88
--- /dev/null
+++ b/docs/website/src/lib/graph-growth.mts
@@ -0,0 +1,52 @@
+interface GrowthField {
+  certificate: string | null;
+  accuracy: { kind: 'exact' | 'upper_bound' | 'unavailable' };
+}
+interface Growth { degree: bigint | null; lead: string }
+type Degree = bigint | null | undefined;
+
+const SUP = '⁰¹²³⁴⁵⁶⁷⁸⁹';
+const sup = (degree: bigint) => degree.toString().replace(/\d/g, digit => SUP.charAt(digit.charCodeAt(0) - 48));
+const memo = new WeakMap<GrowthField, Growth>();
+
+export function growth(field: GrowthField): Growth {
+  const cached = memo.get(field);
+  if (cached) return cached;
+  let out: Growth = { degree: null, lead: 'unavailable' };
+  if (field.certificate != null) {
+    const terms = field.certificate.split(' + ').map(term => {
+      const vars = [...term.matchAll(/([A-Za-z_]\w*)(?:\^([\d.]+))?/g)].map(match => ({
+        // Every successful match includes the mandatory variable capture.
+        v: match[1]!.replace(/^num_/, ''), e: match[2] ? BigInt(match[2]) : 1n,
+      }));
+      return { d: vars.reduce((degree, variable) => degree + variable.e, 0n),
+        txt: vars.map(variable => variable.v + (variable.e === 1n ? '' : sup(variable.e))).join('·') || '1' };
+    });
+    const degree = terms.reduce((max, term) => term.d > max ? term.d : max, 0n);
+    const lead = [...new Set(terms.filter(term => term.d === degree).map(term => term.txt))];
+    out = { degree, lead: (field.accuracy.kind === 'exact' ? 'Θ(' : 'O(') + lead.slice(0, 3).join(' + ')
+      + (lead.length > 3 ? ' + …' : '') + ')' };
+  }
+  memo.set(field, out);
+  return out;
+}
+
+export function pathDegree(profile: { fields: Record<string, GrowthField> }): bigint | null {
+  let max = 0n;
+  for (const field of Object.values(profile.fields)) {
+    const degree = growth(field).degree;
+    if (degree === null) return null;
+    if (degree > max) max = degree;
+  }
+  return max;
+}
+
+export function sizeBadge(degree: Degree): string {
+  return degree == null ? '?' : degree === 0n ? '1' : degree === 1n ? 'n' : 'n' + sup(degree);
+}
+
+export function compareDegrees(left: Degree, right: Degree): number {
+  if (left == null) return right == null ? 0 : 1;
+  if (right == null) return -1;
+  return left < right ? -1 : left > right ? 1 : 0;
+}
diff --git a/docs/website/assets/graph-layout.js b/docs/website/src/lib/graph-layout.js
similarity index 100%
rename from docs/website/assets/graph-layout.js
rename to docs/website/src/lib/graph-layout.js
diff --git a/docs/website/src/lib/path-worker-data.mts b/docs/website/src/lib/path-worker-data.mts
new file mode 100644
index 000000000..f30f98640
--- /dev/null
+++ b/docs/website/src/lib/path-worker-data.mts
@@ -0,0 +1,26 @@
+import type { WasmPathResult } from '../generated/wasm-paths.mjs';
+import type { WasmComparisonResult } from '../generated/wasm-comparison.mjs';
+
+export type PathRequest = { source: number; target: number; limit: number } & (
+  { kind: 'search' } | { kind: 'compare'; cached: WasmPathResult }
+);
+export type PathReply =
+  | { phase: 'paths'; result: WasmPathResult }
+  | { phase: 'comparison'; result: WasmComparisonResult }
+  | { phase: 'paths' | 'comparison'; error: string };
+
+const error = () => new Error('Invalid path worker contract. Reload the current release.');
+export function validatePathRequest(value: PathRequest): PathRequest {
+  if (![value.source, value.target].every(index => Number.isSafeInteger(index) && index >= 0)
+      || !Number.isInteger(value.limit) || value.limit < 1 || value.limit > 999) throw error();
+  return value;
+}
+
+export function validatePathReply(value: PathReply, request: PathRequest, result?: WasmPathResult): PathReply {
+  if ('error' in value) {
+    if (value.phase === 'comparison' && !result?.paths.length) throw error();
+  } else if (value.phase === 'paths') {
+    if (request.kind !== 'search' || result !== undefined) throw error();
+  } else if (!result?.paths.length) throw error();
+  return value;
+}
diff --git a/docs/website/src/lib/variant.mts b/docs/website/src/lib/variant.mts
new file mode 100644
index 000000000..48e6595ec
--- /dev/null
+++ b/docs/website/src/lib/variant.mts
@@ -0,0 +1,2 @@
+export const nodeKey = (node: { name: string; variant: Record<string, string> }): string =>
+  JSON.stringify([node.name, Object.entries(node.variant).sort(([a], [b]) => a < b ? -1 : a > b ? 1 : 0)]);
diff --git a/docs/website/src/pages/details.ts b/docs/website/src/pages/details.ts
new file mode 100644
index 000000000..d6e9713ce
--- /dev/null
+++ b/docs/website/src/pages/details.ts
@@ -0,0 +1,205 @@
+import { validateDetailURL } from '../lib/graph-details-data.mts';
+import type { GraphDetailsIndex } from '../generated/graph-details.mjs';
+
+let detailsIndex: GraphDetailsIndex | undefined;
+const detailCache = new Map<string, Promise<string>>();
+let manifest: Promise<GraphDetailsIndex> | null = null;
+let renderRequest = 0;
+const indexURL = new URL('./assets/graph-details.json', window.location.href);
+function errorMessage(error: unknown): string {
+  return error instanceof Error ? error.message : String(error);
+}
+function normalizeReferenceRoles(container: Element) {
+  for (const wrapper of container.querySelectorAll('sup[role="doc-noteref"], sup[role="doc-backlink"]')) {
+    const role = wrapper.getAttribute('role');
+    if (role) for (const link of wrapper.querySelectorAll('a[href]')) link.setAttribute('role', role);
+    wrapper.removeAttribute('role');
+  }
+}
+export function loadDetailsIndex() {
+  if (detailsIndex) return Promise.resolve(detailsIndex);
+  manifest ||= fetch(indexURL).then(response => {
+    if (!response.ok) throw new Error('Cannot load documentation index. Reload the page to get the current release.');
+    return response.json();
+  }).then((value: GraphDetailsIndex) => {
+    performance.mark('details:index-json-parsed');
+    for (const url of Object.values(value.entries)) {
+      validateDetailURL(url, new URL(window.location.href), new URL('./details/', indexURL));
+    }
+    return detailsIndex = value;
+  }).catch(error => {
+    manifest = null;
+    throw error;
+  });
+  return manifest;
+}
+function loadDetail(key: string): Promise<string> {
+  const url = detailsIndex?.entries[key];
+  if (!url) return Promise.reject(new Error(`Missing detail file: ${key}`));
+  let content = detailCache.get(url);
+  if (!content) {
+    content = fetch(url).then((response) => {
+      if (!response.ok) throw new Error(`Cannot load documentation (${response.status})`);
+      return response.text();
+    }).catch((error) => {
+      detailCache.delete(url);
+      throw error;
+    });
+    detailCache.set(url, content);
+    const oldest = detailCache.keys().next();
+    if (detailCache.size > 24 && !oldest.done) detailCache.delete(oldest.value);
+  } else {
+    detailCache.delete(url);
+    detailCache.set(url, content);
+  }
+  return content;
+}
+
+export async function renderDetails(detail: HTMLElement, title: string, variant: string, key: string, parentKey: string, onProblem: (name: string) => void) {
+  const request = ++renderRequest;
+  detail.replaceChildren();
+  detail.onclick = (event) => {
+    if (!(event.target instanceof Element)) return;
+    const link = event.target.closest('a[href^="#"]');
+    if (!link) return;
+    const anchor = link.getAttribute('href')?.slice(1);
+    if (!anchor) return;
+    const anchors = detailsIndex?.anchors;
+    const key = anchors && Object.hasOwn(anchors, anchor) ? anchors[anchor] : undefined;
+    if (key?.startsWith("problem:") && key !== detail.querySelector("article")?.dataset.contentKey) {
+      event.preventDefault();
+      onProblem(key.slice("problem:".length));
+      return;
+    }
+    if (link.getAttribute("role") === "doc-biblioref") {
+      event.preventDefault();
+      const references = detail.querySelector<HTMLDetailsElement>(".detail-references");
+      if (!references) return;
+      references.open = true;
+      references.scrollIntoView({ block: "nearest" });
+      return;
+    }
+    const target = detail.querySelector(`[id="${CSS.escape(anchor)}"]`);
+    if (!target) {
+      if (key === detail.querySelector("article")?.dataset.contentKey) {
+        event.preventDefault();
+        detail.scrollIntoView({ block: "start" });
+      }
+      return;
+    }
+    event.preventDefault();
+    const references = target.closest("details");
+    if (references) references.open = true;
+    const focus = target.matches('sup') ? target.querySelector('a[href]') : target;
+    if (focus instanceof HTMLElement || focus instanceof SVGElement) {
+      if (!focus.matches('a[href], button, input, select, textarea, summary, [tabindex]')) focus.tabIndex = -1;
+      focus.focus({ preventScroll: true });
+    }
+    target.scrollIntoView({ block: "nearest" });
+  };
+
+  if (title) {
+    const heading = document.createElement("h2");
+    heading.textContent = title;
+    detail.append(heading);
+  }
+  if (variant) {
+    const parameters = document.createElement("p");
+    parameters.className = "detail-variant";
+    parameters.textContent = variant;
+    detail.append(parameters);
+  }
+  const article = document.createElement("article");
+  article.className = "typst-detail";
+  article.textContent = "Loading documentation…";
+  detail.append(article);
+  let index: GraphDetailsIndex;
+  try {
+    index = await loadDetailsIndex();
+  } catch (error) {
+    if (request === renderRequest) {
+      article.textContent = errorMessage(error);
+      article.setAttribute("role", "alert");
+    }
+    return;
+  }
+  if (request !== renderRequest || !article.isConnected) return;
+  const contentKey = index.entries[key] ? key : parentKey;
+  const available = Boolean(index.entries[contentKey]);
+  if (!available) {
+    const note = document.createElement("p");
+    note.className = "detail-source";
+    note.textContent = "No documentation is available for this entry or its parent family.";
+    detail.append(note);
+  }
+  article.dataset.contentKey = contentKey;
+  if (available) {
+    article.textContent = "Loading documentation…";
+    article.setAttribute("aria-busy", "true");
+  }
+  if (!available) { article.remove(); return; }
+  try {
+    const content = await loadDetail(contentKey);
+    if (!article.isConnected) return;
+    // HTML is generated at build time from the repository's Typst source.
+    article.innerHTML = content;
+    // Atlas embeds these sections directly below its page h1; Graph has a drawer h2.
+    if (detail.classList.contains('reference-detail')) for (const heading of article.querySelectorAll('h3')) {
+      const replacement = document.createElement('h2');
+      for (const attribute of heading.attributes) replacement.setAttribute(attribute.name, attribute.value);
+      replacement.append(...heading.childNodes); heading.replaceWith(replacement);
+    }
+    article.querySelectorAll('pre').forEach(code => { code.tabIndex = 0; });
+    normalizeReferenceRoles(article);
+    const citations = new Set([...article.querySelectorAll('a[role="doc-biblioref"]')]
+      .map((link) => link.getAttribute('href')?.slice(1)));
+    if (citations.size) {
+      const references = document.createElement("details");
+      references.className = "detail-references";
+      const summary = document.createElement('summary');
+      summary.textContent = 'References';
+      const body = document.createElement('div');
+      references.append(summary, body);
+      article.after(references);
+      let loaded = false;
+      references.addEventListener("toggle", async () => {
+        if (!references.open || loaded) return;
+        body.textContent = "Loading references…";
+        try {
+          body.innerHTML = await loadDetail("references");
+          body.querySelectorAll("li").forEach((item) => {
+            if (!citations.has(item.id)) item.remove();
+          });
+          loaded = true;
+        } catch (error) {
+          body.textContent = errorMessage(error);
+          body.setAttribute("role", "alert");
+        }
+      });
+    }
+    if (article.querySelector('a[role="doc-noteref"]')) {
+      const notes = document.createElement("aside");
+      notes.className = "typst-detail detail-footnotes";
+      try {
+        notes.innerHTML = await loadDetail("footnotes");
+        normalizeReferenceRoles(notes);
+        const used = new Set([...article.querySelectorAll('a[role="doc-noteref"]')].map((link) => link.getAttribute('href')?.slice(1)));
+        notes.querySelectorAll('li').forEach((item) => {
+          if (!used.has(item.id)) item.remove();
+        });
+      } catch (error) {
+        // The article is already rendered; only its footnotes degrade.
+        notes.textContent = errorMessage(error);
+        notes.setAttribute("role", "alert");
+      }
+      if (!article.isConnected) return;
+      article.after(notes);
+    }
+  } catch (error) {
+    if (!article.isConnected) return;
+    article.textContent = errorMessage(error);
+    article.setAttribute("role", "alert");
+  } finally {
+    article.removeAttribute("aria-busy");
+  }
+}
diff --git a/docs/website/src/pages/graph-scene.ts b/docs/website/src/pages/graph-scene.ts
new file mode 100644
index 000000000..636ab61a7
--- /dev/null
+++ b/docs/website/src/pages/graph-scene.ts
@@ -0,0 +1,309 @@
+// The scene is small and already laid out at build time; SVG owns hit testing and painting.
+export interface Point { x: number; y: number }
+export interface SceneNodeInput extends Point {
+  id: string; label: string; size: number; color: string; deg: number;
+}
+export interface SceneNode extends Omit<SceneNodeInput, 'label'> {
+  shape: SVGGElement; label: SVGTextElement; labelText: string; routeLabel: string;
+  labelKey: string | null; width: number; height: number;
+}
+export interface SceneEdge {
+  id: string; source: SceneNode; target: SceneNode; shape: SVGLineElement;
+  label?: never;
+}
+export type SceneItem = SceneNode | SceneEdge;
+interface Rectangle extends Point { w: number; h: number }
+interface Bounds { x1: number; x2: number; y1: number; y2: number }
+interface Gesture { item: SceneItem | undefined; moved: boolean; start: Point }
+
+export class GraphScene {
+  zoom: number;
+  pan: Point;
+  animation: number;
+  svg: SVGSVGElement;
+  world: SVGGElement;
+  nodes: SceneNode[];
+  edges: SceneEdge[];
+  byId: Map<string, SceneItem>;
+  elements: SceneItem[];
+  measure: CanvasRenderingContext2D;
+  tabStop: SceneNode;
+  visibleRect?: () => Rectangle;
+  onNodeTap?: (node: SceneNode, options?: { keyboard: boolean }) => void;
+  onEdgeTap?: (edge: SceneEdge) => void;
+  onBackgroundTap?: () => void;
+  onChange?: () => void;
+  onDrag?: (node: SceneNode) => void;
+  onHover?: (node: SceneNode, over: boolean) => void;
+
+  constructor(container: HTMLElement, nodes: SceneNodeInput[], edges: { s: string; t: string }[]) {
+    const make = <Tag extends keyof SVGElementTagNameMap>(tag: Tag, attrs: Record<string, string | number> = {}) => {
+      const node = document.createElementNS('http://www.w3.org/2000/svg', tag);
+      for (const [key, value] of Object.entries(attrs)) node.setAttribute(key, String(value));
+      return node;
+    };
+    this.zoom = 1; this.pan = {x: 0, y: 0}; this.animation = 0;
+    this.svg = make('svg', {class: 'graph-scene', role: 'group',
+      'aria-label': 'Problem families and directed reductions. Arrows move between spatial neighbours. Page Up and Page Down visit every problem. Home and End jump to the first and last problem. Enter or Space opens controls.'});
+    this.world = make('g');
+    const defs = make('defs'), marker = make('marker', {id: 'route-arrow', viewBox: '0 -5 10 10', refX: 9, refY: 0,
+      markerWidth: 11, markerHeight: 11, orient: 'auto', markerUnits: 'userSpaceOnUse'});
+    marker.append(make('path', {d: 'M0,-4.5 L10,0 L0,4.5 Z', fill: 'var(--accent)'}));
+    defs.append(marker); this.svg.append(defs, this.world); container.append(this.svg);
+    this.nodes = nodes.map(data => {
+      const shape = make('g', {class: 'scene-node', 'data-node': data.id, role: 'button', tabindex: -1,
+        'aria-haspopup': 'dialog', 'aria-label': data.label});
+      const halo = make('circle', {class: 'node-halo', r: data.size / 2 + 6});
+      const circle = make('circle', {class: 'node-disc', r: data.size / 2, fill: data.color});
+      const label = make('text', {class: 'node-label', 'text-anchor': 'middle'});
+      shape.append(halo, circle, label);
+      return {...data, shape, label, labelText: data.label, routeLabel: data.label, labelKey: null, width: 0, height: 0};
+    });
+    this.byId = new Map(this.nodes.map(n => [n.id, n]));
+    this.edges = edges.map(({s, t}) => {
+      const source = this.byId.get(s), target = this.byId.get(t);
+      if (!source?.label || !target?.label) throw new Error('A scene edge references a missing node');
+      const edge = {id: s + '→' + t, source, target,
+        shape: make('line', {class: 'scene-edge', 'data-edge': s + '→' + t, 'aria-hidden': 'true'})};
+      this.byId.set(edge.id, edge); this.world.append(edge.shape); return edge;
+    });
+    for (const node of this.nodes) this.world.append(node.shape);
+    this.elements = [...this.nodes, ...this.edges];
+    const measure = document.createElement('canvas').getContext('2d');
+    if (!measure) throw new Error('Canvas text measurement is unavailable');
+    this.measure = measure;
+    this.updatePositions();
+
+    const point = (e: MouseEvent): Point => { const r = this.svg.getBoundingClientRect(); return {x: e.clientX - r.x, y: e.clientY - r.y}; };
+    const pointers = new Map<number, Point>();
+    let gesture: Gesture | undefined;
+    this.svg.addEventListener('pointerdown', e => {
+      if (e.button !== 0) return;
+      this.stop();
+      const p = point(e); pointers.set(e.pointerId, p);
+      const target = e.target instanceof Element ? e.target.closest('[data-node], [data-edge]') : null;
+      const id = target?.getAttribute('data-node') || target?.getAttribute('data-edge');
+      gesture = {item: id ? this.byId.get(id) : undefined,
+        moved: pointers.size > 1, start: p};
+      this.svg.setPointerCapture(e.pointerId);
+    });
+    this.svg.addEventListener('pointermove', e => {
+      const old = pointers.get(e.pointerId);
+      if (!old || !gesture) return;
+      const before = [...pointers.values()], p = point(e);
+      pointers.set(e.pointerId, p);
+      const dx = p.x - old.x, dy = p.y - old.y;
+      if (pointers.size > 1) {
+        const after = [...pointers.values()];
+        const [first, second] = before, [nextFirst, nextSecond] = after;
+        if (!first || !second || !nextFirst || !nextSecond) return;
+        const center = (a: Point, b: Point): Point => ({x: (a.x + b.x) / 2, y: (a.y + b.y) / 2});
+        const distance = (a: Point, b: Point) => Math.hypot(a.x - b.x, a.y - b.y);
+        const a = center(first, second), b = center(nextFirst, nextSecond), previous = distance(first, second);
+        if (previous) this.zoomAt(this.zoom * distance(nextFirst, nextSecond) / previous, a);
+        this.setViewport(this.zoom, {x: this.pan.x + b.x - a.x, y: this.pan.y + b.y - a.y});
+        gesture.item = undefined; gesture.moved = true;
+      } else if (Math.hypot(p.x - gesture.start.x, p.y - gesture.start.y) > 3 || gesture.moved) {
+        gesture.moved = true;
+        if (gesture.item?.label) {
+          this.moveNode(gesture.item, dx, dy);
+        } else this.setViewport(this.zoom, {x: this.pan.x + dx, y: this.pan.y + dy});
+      }
+    });
+    const release = (e: PointerEvent) => {
+      if (!pointers.has(e.pointerId) || !gesture) return;
+      pointers.delete(e.pointerId);
+      if (e.type === 'pointerup' && !gesture.moved) {
+        if (gesture.item?.label) this.onNodeTap?.(gesture.item);
+        else if (gesture.item) this.onEdgeTap?.(gesture.item);
+        else this.onBackgroundTap?.();
+      }
+      if (pointers.size) gesture.moved = true;
+    };
+    this.svg.addEventListener('pointerup', release);
+    this.svg.addEventListener('pointercancel', release);
+    // Roving tabindex: one Tab stop for the whole graph, arrows move between spatial neighbours.
+    const first = this.nodes[0];
+    if (!first) throw new Error('A scene requires at least one node');
+    this.tabStop = first;
+    this.tabStop.shape.setAttribute('tabindex', '0');
+    this.svg.addEventListener('focusin', e => {
+      const node = this.nodeOf(e.target);
+      if (!node) return;
+      this.stop();
+      this.setTabStop(node);
+      node.shape.classList.add('focused');
+      node.shape.setAttribute('aria-label', this.describe(node));
+      this.reveal(node);
+      this.onChange?.();
+    });
+    this.svg.addEventListener('focusout', e => {
+      this.nodeOf(e.target)?.shape.classList.remove('focused');
+      this.onChange?.();
+    });
+    this.svg.addEventListener('click', e => {
+      const node = this.nodeOf(e.target);
+      if (node && e.detail === 0) this.onNodeTap?.(node, {keyboard: true});
+    });
+    this.svg.addEventListener('keydown', e => {
+      const node = this.nodeOf(e.target);
+      if (!node || e.altKey || e.ctrlKey || e.metaKey) return;
+      if (e.key === ' ') { e.preventDefault(); return; }
+      if (e.key === 'Enter') { e.preventDefault(); this.onNodeTap?.(node, {keyboard: true}); return; }
+      const index = this.nodes.indexOf(node);
+      const stops: Record<string, number> = {Home: 0, End: this.nodes.length - 1,
+        PageDown: (index + 1) % this.nodes.length,
+        PageUp: (index + this.nodes.length - 1) % this.nodes.length};
+      const next = stops[e.key];
+      if (next != null) { e.preventDefault(); this.nodes[next]?.shape.focus(); return; }
+      const directions: Record<string, [number, number]> = {ArrowRight: [1, 0], ArrowLeft: [-1, 0], ArrowDown: [0, 1], ArrowUp: [0, -1]};
+      const direction = directions[e.key];
+      if (!direction) return;
+      e.preventDefault();
+      this.neighbour(node, direction)?.shape.focus();
+    });
+    this.svg.addEventListener('keyup', e => {
+      const node = this.nodeOf(e.target);
+      if (node && e.key === ' ' && !e.altKey && !e.ctrlKey && !e.metaKey) {
+        e.preventDefault(); this.onNodeTap?.(node, {keyboard: true});
+      }
+    });
+    this.svg.addEventListener('wheel', e => {
+      e.preventDefault(); this.stop(); this.zoomAt(this.zoom * Math.exp(-e.deltaY * .002), point(e));
+    }, {passive: false});
+    for (const [event, over] of [['pointerover', true], ['pointerout', false]] as const) this.svg.addEventListener(event, e => {
+      const node = this.nodeOf(e.target);
+      if (node && (!(e.relatedTarget instanceof Node) || !node.shape.contains(e.relatedTarget))) this.onHover?.(node, over);
+    });
+  }
+
+  nodeOf(target: EventTarget | null): SceneNode | undefined {
+    const id = target instanceof Element ? target.closest('[data-node]')?.getAttribute('data-node') : null;
+    const item = id ? this.byId.get(id) : undefined;
+    return item?.label ? item : undefined;
+  }
+  setTabStop(node: SceneNode) {
+    if (this.tabStop === node) return;
+    this.tabStop.shape.setAttribute('tabindex', '-1');
+    node.shape.setAttribute('tabindex', '0');
+    this.tabStop = node;
+  }
+  // The spoken name includes whatever the route painting says about the node.
+  describe(node: SceneNode) {
+    const roles = ([['start', 'start of the route'], ['end', 'end of the route'], ['route', 'on the selected route']] as const)
+      .filter(([name]) => this.has(node, name)).map(([, text]) => text);
+    return [node.routeLabel.replace('\n', ', '), ...roles].join(', ');
+  }
+  // Nearest node inside a 90° cone around the arrow direction, measured on screen-independent world coordinates.
+  neighbour(node: SceneNode, [dx, dy]: [number, number]) {
+    let best: SceneNode | undefined, bestScore = Infinity;
+    for (const other of this.nodes) {
+      if (other === node) continue;
+      const along = (other.x - node.x) * dx + (other.y - node.y) * dy;
+      const across = Math.abs((other.x - node.x) * dy - (other.y - node.y) * dx);
+      if (along <= 0 || across > along) continue;
+      const score = along + 2 * across;
+      if (score < bestScore) { best = other; bestScore = score; }
+    }
+    return best;
+  }
+  // Keyboard focus must never land off-screen: pan the minimum distance to bring the node into view.
+  reveal(node: SceneNode) {
+    const box = this.svg.getBoundingClientRect(), p = this.position(node);
+    const r = this.visibleRect?.() || {x: 0, y: 0, w: box.width, h: box.height};
+    this.labelBox(node);
+    const radius = (node.size / 2 + 6) * this.zoom;
+    const side = Math.min(Math.max(48, node.width / 2 + 12, radius + 12), r.w / 2);
+    const top = Math.min(Math.max(48, radius + 12), r.h / 2);
+    const bottom = Math.min(Math.max(48, node.size / 2 * this.zoom + node.height + 17), r.h / 2);
+    const shift = (value: number, low: number, high: number) => value < low ? low - value : value > high ? high - value : 0;
+    const x = shift(p.x, r.x + side, r.x + r.w - side), y = shift(p.y, r.y + top, r.y + r.h - bottom);
+    if (x || y) this.setViewport(this.zoom, {x: this.pan.x + x, y: this.pan.y + y});
+  }
+  has(item: SceneItem, name: string) { return item.shape.classList.contains(name); }
+  classes(items: SceneItem[], remove: string, add = '') {
+    const removed = remove.split(' ').filter(Boolean), added = add.split(' ').filter(Boolean);
+    for (const item of items) {
+      for (const name of removed) if (this.has(item, name)) item.shape.classList.remove(name);
+      for (const name of added) if (!this.has(item, name)) item.shape.classList.add(name);
+    }
+  }
+  updatePositions() {
+    for (const node of this.nodes) node.shape.setAttribute('transform', `translate(${node.x} ${node.y})`);
+    for (const edge of this.edges) {
+      const a = edge.source, b = edge.target, d = Math.hypot(b.x-a.x, b.y-a.y) || 1, r = b.size/2 + 4;
+      edge.shape.setAttribute('x1', String(a.x)); edge.shape.setAttribute('y1', String(a.y));
+      edge.shape.setAttribute('x2', String(b.x - (b.x-a.x)*r/d)); edge.shape.setAttribute('y2', String(b.y - (b.y-a.y)*r/d));
+    }
+  }
+  moveNode(node: SceneNode, dx: number, dy: number) {
+    this.stop();
+    node.x += dx / this.zoom; node.y += dy / this.zoom;
+    this.updatePositions(); this.onDrag?.(node); this.onChange?.();
+  }
+  position(item: SceneItem): Point {
+    const x = item.label ? item.x : (item.source.x + item.target.x) / 2;
+    const y = item.label ? item.y : (item.source.y + item.target.y) / 2;
+    return {x: x * this.zoom + this.pan.x, y: y * this.zoom + this.pan.y};
+  }
+  bounds(items: SceneItem[], rendered?: false): Bounds & { w: number; h: number };
+  bounds(items: SceneItem[], rendered: true): Bounds;
+  bounds(items: SceneItem[], rendered = false) {
+    const nodes = items.flatMap(n => n.label ? [n] : [n.source, n.target]);
+    const x1 = Math.min(...nodes.map(n => n.x - n.size/2)), x2 = Math.max(...nodes.map(n => n.x + n.size/2));
+    const y1 = Math.min(...nodes.map(n => n.y - n.size/2)), y2 = Math.max(...nodes.map(n => n.y + n.size/2));
+    return rendered ? {x1: x1*this.zoom+this.pan.x, x2: x2*this.zoom+this.pan.x,
+      y1: y1*this.zoom+this.pan.y, y2: y2*this.zoom+this.pan.y} : {x1, x2, y1, y2, w: x2-x1, h: y2-y1};
+  }
+  setViewport(zoom: number, pan: Point) {
+    this.zoom = zoom; this.pan = pan;
+    this.world.setAttribute('transform', `translate(${pan.x} ${pan.y}) scale(${zoom})`);
+    this.onChange?.();
+  }
+  zoomAt(zoom: number, p: Point) {
+    zoom = Math.max(.1, Math.min(3, zoom));
+    const scale = zoom / this.zoom;
+    this.setViewport(zoom, {x: p.x-(p.x-this.pan.x)*scale, y: p.y-(p.y-this.pan.y)*scale});
+  }
+  stop() { cancelAnimationFrame(this.animation); this.animation = 0; }
+  frame(zoom: number, pan: Point, animate: boolean) {
+    this.stop();
+    if (!animate) { this.setViewport(zoom, pan); performance.mark('graph:camera-settled'); return; }
+    const start = performance.now(), z = this.zoom, p = this.pan;
+    const step = (now: number) => {
+      const t = Math.min(1, (now-start)/450), ease = t < .5 ? 4*t*t*t : 1-(-2*t+2)**3/2;
+      this.setViewport(z+(zoom-z)*ease, {x:p.x+(pan.x-p.x)*ease, y:p.y+(pan.y-p.y)*ease});
+      this.animation = t < 1 ? requestAnimationFrame(step) : 0;
+      if (t === 1) performance.mark('graph:camera-settled');
+    };
+    this.animation = requestAnimationFrame(step);
+  }
+  labelBox(node: SceneNode): Bounds {
+    const important = ['route', 'start', 'end', 'hover', 'focused'].some(c => this.has(node, c));
+    const size = important ? 12 : 11, text = important ? node.routeLabel : node.labelText;
+    const key = size + ':' + text;
+    if (node.labelKey !== key) {
+      node.labelKey = key;
+      this.measure.font = `500 ${size}px "DM Sans", sans-serif`;
+      const lines = [];
+      for (const paragraph of text.split('\n')) {
+        let line = '';
+        for (const word of paragraph.split(' ')) {
+          if (line && this.measure.measureText(line+' '+word).width > 180) { lines.push(line); line = word; }
+          else line += (line ? ' ' : '') + word;
+        }
+        lines.push(line);
+      }
+      node.width = Math.max(...lines.map(line => this.measure.measureText(line).width));
+      node.height = lines.length * size * 1.25;
+      node.label.replaceChildren(...lines.map((line, i) => {
+        const span = document.createElementNS('http://www.w3.org/2000/svg', 'tspan');
+        span.setAttribute('x', '0'); span.setAttribute('y', String(5+size+i*size*1.25)); span.textContent = line; return span;
+      }));
+      node.label.setAttribute('font-size', String(size));
+    }
+    node.label.setAttribute('transform', `translate(0 ${node.size/2}) scale(${1/this.zoom})`);
+    const p = this.position(node), top = p.y + node.size/2*this.zoom + 5;
+    return {x1:p.x-node.width/2-3, x2:p.x+node.width/2+3, y1:top-3, y2:top+node.height+3};
+  }
+}
diff --git a/docs/website/src/pages/graph-startup.ts b/docs/website/src/pages/graph-startup.ts
new file mode 100644
index 000000000..8df6b26a2
--- /dev/null
+++ b/docs/website/src/pages/graph-startup.ts
@@ -0,0 +1,24 @@
+import type { GraphSceneData } from '../generated/graph-scene.mjs';
+
+// Start independent downloads before the renderer finishes loading.
+export const graphStartup: {scene: Promise<GraphSceneData>; worker: Worker | null} = {
+  scene: fetch(document.body.dataset.scene!).then(async (response) => {
+    if (!response.ok || !response.body) throw new Error(`Cannot load graph (${response.status})`);
+    const text = await new Response(response.body.pipeThrough(new DecompressionStream('gzip'))).text();
+    performance.mark('graph:scene-decoded');
+    const scene = JSON.parse(text) as GraphSceneData;
+    performance.mark('graph:scene-json-parsed');
+    return scene;
+  }),
+  worker: null,
+};
+graphStartup.scene.catch(() => {});
+try {
+  const worker = graphStartup.worker = new Worker(new URL('../workers/path-worker.ts', import.meta.url), {type: 'module'});
+  performance.mark('graph:worker-started');
+  worker.addEventListener('error', (event) => {
+    event.preventDefault();
+    if (graphStartup.worker === worker) { worker.terminate(); graphStartup.worker = null; }
+  });
+}
+catch { /* Path search reports worker creation errors when requested. */ }
diff --git a/docs/website/src/pages/graph.ts b/docs/website/src/pages/graph.ts
new file mode 100644
index 000000000..db49746b8
--- /dev/null
+++ b/docs/website/src/pages/graph.ts
@@ -0,0 +1,650 @@
+import { graphStartup } from './graph-startup.ts';
+import { renderDetails } from './details.ts';
+import { GraphScene, type SceneNode, type SceneItem } from "./graph-scene.ts";
+import { growth, pathDegree, sizeBadge, compareDegrees } from "../lib/graph-growth.mts";
+import { validatePathReply, type PathRequest, type PathReply } from '../lib/path-worker-data.mts';
+
+import type { Endpoint, Route, Step, WasmPathResult } from '../generated/wasm-paths.mjs';
+import type { WasmComparisonResult } from '../generated/wasm-comparison.mjs';
+import type { GraphSceneData } from '../generated/graph-scene.mjs';
+
+type Side = 'source' | 'target';
+interface Family { name: string; category: GraphSceneData['nodes'][number]['category']; variants: number[]; nbrs: Set<string> }
+type PathResult = WasmPathResult & { polynomial_comparison?: WasmComparisonResult; order?: number[] };
+interface State { source: number | null; target: number | null; limit: number; result: PathResult | null;
+  selected: number | null; picked: boolean; showSlower: boolean; busy: boolean }
+
+type Bounds = ReturnType<GraphScene['labelBox']>;
+
+(async () => {
+"use strict";
+performance.mark("graph:script", {detail: {eager_worker: Boolean(graphStartup.worker)}});
+const $ = <T extends HTMLElement = HTMLElement>(s: string) => document.querySelector<T>(s)!;
+const el = <T extends keyof HTMLElementTagNameMap>(tag: T, cls?: string, text?: string) => { const n = document.createElement(tag); if (cls) n.className = cls; if (text != null) n.textContent = text; return n; };
+const D = window.REDUCTIONS = await graphStartup.scene;
+performance.mark("graph:scene-parsed");
+const defaults = Object.fromEntries(D.nodes.flatMap((n, i) => n.default ? [[n.name, i]] : []));
+const aliasMap = D.aliases;
+const reduced = matchMedia("(prefers-reduced-motion: reduce)");
+const phone = matchMedia("(max-width: 760px)");
+// Keep the minimum supported 320px graph viewport beside the 392px and 456px side-panel areas.
+const modalDetails = matchMedia("(max-width: 1167px)");
+
+// The build validates scene references; the engine owns path correctness.
+/* ---------- Registry model ---------- */
+const display = (name: string) => name.replace(/([a-z0-9])([A-Z])/g, "$1 $2").replace(/([A-Z])([A-Z][a-z])/g, "$1 $2");
+const families = new Map<string, Family>();
+D.nodes.forEach((n, i) => {
+  if (!families.has(n.name)) families.set(n.name, { name: n.name, category: n.category, variants: [], nbrs: new Set() });
+  families.get(n.name)!.variants.push(i);
+});
+const famEdges = new Map<string, {s: string; t: string}>();
+D.edges.forEach((e) => {
+  const s = D.nodes[e.source]!.name, t = D.nodes[e.target]!.name;
+  if (s === t) return;
+  famEdges.set(s + "→" + t, { s, t });
+  families.get(s)!.nbrs.add(t); families.get(t)!.nbrs.add(s);
+});
+const multi = (name: string) => families.get(name)!.variants.length > 1;
+const keyOf = (node: Endpoint) => node.name + "|" + Object.entries(node.variant).sort().map(([k, v]) => k + "=" + v).join(",");
+const indexOf = new Map(D.nodes.map((n, i) => [keyOf(n), i]));
+
+/* Keyed variant text, e.g. graph: KingsSubgraph  weight: i64 */
+function kvNode(variant: Endpoint['variant']) {
+  const span = el("span", "kv");
+  Object.entries(variant).forEach(([k, v], i) => { if (i) span.append("   "); span.append(el("i", "", k + ": "), v); });
+  return span;
+}
+
+const prettyField = (f: string) => f.replace(/^num_/, "").replaceAll("_", " ");
+
+/* ---------- Graph ---------- */
+const nodeSize = (deg: number) => Math.max(6, Math.min(22, 6 + 2.4 * Math.sqrt(deg)));
+const pos = new Map<string, {x: number; y: number}>();
+for (const f of families.values()) pos.set(f.name, { x: D.layout[f.name]!.x * 1.6, y: D.layout[f.name]!.y * 1.6 });
+const cat = { graph: "#a9d68a", formula: "#8cc4c7", set: "#e0a988", algebraic: "#e2cf73", misc: "#c39bd3" };
+const scene = new GraphScene($("#cy"), [...families.values()].map(f => ({id: f.name, label: display(f.name),
+  size: nodeSize(f.nbrs.size), deg: f.nbrs.size, color: cat[f.category] || cat.misc, ...pos.get(f.name)!})), [...famEdges.values()]);
+performance.mark("graph:renderer-created");
+performance.mark("graph:constructed");
+
+function freeRect() {
+  const W = innerWidth, H = innerHeight, top = $(".site-header").getBoundingClientRect().bottom;
+  if (phone.matches) return { x: 0, y: top, w: W, h: Math.max(1, $(".panel").getBoundingClientRect().top - top) };
+  const right = $("#details-drawer").hidden || modalDetails.matches ? W : $("#details-drawer").getBoundingClientRect().left - 16;
+  return { x: 392, y: top, w: Math.max(1, right - 392), h: H - top };
+}
+scene.visibleRect = freeRect;
+function frame(eles: SceneItem[], maxZoom = 1.3, animate = !reduced.matches) {
+  if (!eles || !eles.length) return;
+  const r = freeRect(), b = scene.bounds(eles), pad = 90;
+  const zoom = Math.max(0.1, Math.min((r.w - 2 * pad) / Math.max(b.w, 1), (r.h - 2 * pad) / Math.max(b.h, 1), maxZoom));
+  const pan = { x: r.x + r.w / 2 - (b.x1 + b.x2) / 2 * zoom, y: r.y + r.h / 2 - (b.y1 + b.y2) / 2 * zoom };
+  scene.frame(zoom, pan, animate);
+}
+
+/* Labels keep a constant screen size; important labels are placed first and any label that would collide is skipped. */
+let labelRaf = 0;
+const scheduleLabels = () => { cancelAnimationFrame(labelRaf); labelRaf = requestAnimationFrame(placeLabels); };
+function placeLabels() {
+  const r = freeRect(), boxes: Bounds[] = [];
+  const box = (n: SceneNode) => scene.labelBox(n);
+  const important = (n: SceneNode) => ["route", "start", "end", "hover", "focused"].some(c => scene.has(n, c));
+  const fits = (b: Bounds) => b.x1 > r.x + 4 && b.x2 < r.x + r.w - 4 && b.y1 > r.y + 4 && b.y2 < r.y + r.h - 4;
+  const hit = (b: Bounds) => boxes.some(o => b.x1 < o.x2 + 6 && b.x2 > o.x1 - 6 && b.y1 < o.y2 + 4 && b.y2 > o.y1 - 4);
+  scene.classes(scene.nodes, "named");
+  scene.nodes.filter(important).forEach(n => boxes.push(box(n)));
+  const named: SceneNode[] = [];
+  scene.nodes.filter(n => !important(n) && !scene.has(n, "dim")).sort((a,b) => b.deg-a.deg).forEach(n => {
+    const b = box(n);
+    if (fits(b) && !hit(b)) { boxes.push(b); named.push(n); }
+  });
+  scene.classes(named, "", "named");
+  placePop();
+}
+scene.onChange = scheduleLabels;
+scene.onDrag = () => { scheduleLabels(); placePop(); };
+scene.onHover = (n, over) => {
+  scene.classes([n], over ? "" : "hover", over ? "hover" : "");
+  if (!state.result) {
+    if (over) {
+      scene.classes(scene.elements.filter(e => e !== n && !families.get(n.id)!.nbrs.has(e.id)), "", "dim");
+      scene.classes(scene.edges.filter(e => e.source === n || e.target === n), "dim", "nbr");
+    } else scene.classes(scene.elements, "dim nbr");
+  }
+  scheduleLabels();
+};
+
+/* ---------- State ---------- */
+const state: State = { source: null, target: null, limit: 20, result: null, selected: null, picked: false, showSlower: false, busy: false };
+
+/* Variant options: one row of pills per variant key. Picking a value keeps the other keys when such a variant exists. */
+function focusedVariantGroup(root: HTMLElement) {
+  const active = document.activeElement;
+  return active && root.contains(active) ? active.closest('[role="group"]')?.getAttribute('aria-label') : null;
+}
+function restoreVariantGroup(root: HTMLElement, name: string | null | undefined) {
+  if (name) [...root.querySelectorAll('[role="group"]')].find(group => group.getAttribute('aria-label') === name)
+    ?.querySelector<HTMLButtonElement>('button[aria-pressed="true"]')?.focus({preventScroll: true});
+}
+function variantOptions(container: HTMLElement, index: number, onPick: (index: number) => void) {
+  const focused = focusedVariantGroup(container);
+  container.replaceChildren();
+  const fam = families.get(D.nodes[index]!.name)!;
+  const cur = D.nodes[index]!.variant;
+  const keys = [...new Set(fam.variants.flatMap((i) => Object.keys(D.nodes[i]!.variant)))];
+  keys.forEach((k) => {
+    const values = [...new Set(fam.variants.map((i) => D.nodes[i]!.variant[k]).filter(Boolean))];
+    if (values.length < 2) return;
+    const row = el("div", "opt-row"); row.setAttribute("role", "group"); row.setAttribute("aria-label", k);
+    row.append(el("span", "opt-key", k));
+    values.forEach((v) => {
+      const b = el("button", "opt", v); b.type = "button";
+      b.setAttribute("aria-pressed", String(cur[k] === v));
+      b.addEventListener("pointerdown", (ev) => ev.preventDefault());
+      b.addEventListener("click", (ev) => {
+        ev.stopPropagation();
+        const score = (i: number) => Object.entries(cur).filter(([kk, vv]) => kk !== k && D.nodes[i]!.variant[kk] === vv).length + (i === defaults[fam.name]! ? 0.5 : 0);
+        onPick(fam.variants.filter((i) => D.nodes[i]!.variant[k] === v).sort((a, b) => score(b) - score(a))[0]!);
+      });
+      row.append(b);
+    });
+    container.append(row);
+  });
+  container.hidden = !container.childElementCount;
+  restoreVariantGroup(container, focused);
+}
+
+function syncEnds() {
+  for (const side of ["source", "target"] as const) {
+    const input = $<HTMLInputElement>("#" + side), opts = $("#" + side + "-options"), i = state[side];
+    if (document.activeElement !== input) input.value = i == null ? "" : display(D.nodes[i]!.name);
+    if (i == null) { opts.hidden = true; opts.replaceChildren(); } else variantOptions(opts, i, (j) => setEnd(side, j));
+  }
+  $("#swap").style.top = ($(".end.to").offsetTop - 15) + "px";
+}
+
+function setEnd(side: Side, index: number) {
+  state[side] = index;
+  closePop();
+  syncEnds();
+  if (state.source != null && state.target != null) run();
+  else {
+    state.result = null; paintGraph(); renderResults();
+    frame([scene.byId.get(D.nodes[index]!.name)!], 1.2);
+    if (side === "source") $("#target").focus();
+  }
+}
+
+/* ---------- Search fields ---------- */
+let suggestFor: Side | null = null, suggestRows: Family[] = [], active = 0;
+function matches(q: string) {
+  q = q.trim().toLowerCase();
+  const all = [...families.values()];
+  if (!q) return all.sort((a, b) => b.nbrs.size - a.nbrs.size).slice(0, 7);
+  const rank = (f: Family) => {
+    const al = (aliasMap[f.name] || []).map((a) => a.toLowerCase()), name = display(f.name).toLowerCase();
+    if (al.includes(q)) return 0;
+    if (name.startsWith(q)) return 1;
+    if (name.includes(q) || f.name.toLowerCase().includes(q)) return 2;
+    if (al.some((a) => a.startsWith(q))) return 3;
+    return 9;
+  };
+  return all.map((f) => [rank(f), f] as const).filter(([r]) => r < 9).sort((a, b) => a[0] - b[0] || b[1].nbrs.size - a[1].nbrs.size).slice(0, 7).map(([, f]) => f);
+}
+function showSuggest(side: Side) {
+  suggestFor = side;
+  const input = $<HTMLInputElement>("#" + side), box = $("#suggest");
+  suggestRows = matches(input.value === (state[side] == null ? "" : display(D.nodes[state[side]]!.name)) ? "" : input.value);
+  active = 0;
+  box.replaceChildren();
+  if (!suggestRows.length) {
+    const empty = el("div", "note", "No matching problem");
+    empty.setAttribute("role", "option"); empty.setAttribute("aria-disabled", "true"); box.append(empty);
+  }
+  $("#search-status").textContent = suggestRows.length ? "" : "No matching problem";
+  suggestRows.forEach((f, i) => {
+    const b = el("button"); b.type = "button"; b.setAttribute("role", "option"); b.id = "opt-" + i;
+    b.append(el("span", "", display(f.name)));
+    const al = (aliasMap[f.name] || [])[0]; if (al) b.append(el("small", "", al));
+    b.addEventListener("pointerdown", (e) => { e.preventDefault(); pick(i); });
+    box.append(b);
+  });
+  const end = input.closest<HTMLElement>(".end")!;
+  box.style.top = (end.offsetTop + 44) + "px";
+  box.hidden = false; input.setAttribute("aria-expanded", "true");
+  markActive();
+}
+function markActive() {
+  [...$("#suggest").querySelectorAll("button")].forEach((b, i) => b.setAttribute("aria-selected", String(i === active)));
+  for (const side of ["source", "target"] as const) $("#" + side).removeAttribute("aria-activedescendant");
+  if (suggestFor && suggestRows.length) $("#" + suggestFor).setAttribute("aria-activedescendant", "opt-" + active);
+}
+function hideSuggest() {
+  $("#suggest").hidden = true; $("#search-status").textContent = "";
+  for (const side of ["source", "target"] as const) {
+    $("#" + side).setAttribute("aria-expanded", "false"); $("#" + side).removeAttribute("aria-activedescendant");
+  }
+  suggestFor = null;
+}
+function pick(i: number) { const f = suggestRows[i]; if (!f) return; const side = suggestFor!; hideSuggest(); $("#" + side).blur(); setEnd(side, defaults[f.name]!); }
+for (const side of ["source", "target"] as const) {
+  const input = $<HTMLInputElement>("#" + side);
+  input.addEventListener("focus", () => { input.select(); showSuggest(side); });
+  input.addEventListener("input", () => showSuggest(side));
+  input.addEventListener("blur", () => setTimeout(() => {
+    if (document.activeElement !== input && suggestFor === side) hideSuggest();
+    syncEnds();
+  }, 0));
+  input.addEventListener("keydown", (e) => {
+    if (e.key === "ArrowDown" || e.key === "ArrowUp") { e.preventDefault(); active = (active + (e.key === "ArrowDown" ? 1 : -1) + suggestRows.length) % Math.max(1, suggestRows.length); markActive(); }
+    else if (e.key === "Enter") { e.preventDefault(); pick(active); }
+    else if (e.key === "Escape") { hideSuggest(); input.blur(); }
+  });
+}
+$("#swap").addEventListener("click", () => { [state.source, state.target] = [state.target, state.source]; syncEnds(); if (state.source != null && state.target != null) run(); });
+
+/* ---------- Node popover ---------- */
+let popNode: SceneNode | null = null, popIndex: number | null = null;
+function routeVariantOf(name: string) {
+  const r = state.result?.paths[state.selected! - 1]; if (!r) return null;
+  const hit = endpoints(r).find((e) => e.name === name);
+  return hit ? indexOf.get(keyOf(hit)) : null;
+}
+function openPop(node: SceneNode, {keyboard = false} = {}) {
+  popNode = node;
+  const name = node.id;
+  popIndex = [state.source, state.target].find((i) => i != null && D.nodes[i]!.name === name) ?? routeVariantOf(name) ?? defaults[name]!;
+  renderPop();
+  if (keyboard) $("#pop button").focus({preventScroll: true});
+}
+function renderPop() {
+  const pop = $("#pop"), focusGroup = focusedVariantGroup(pop);
+  pop.replaceChildren();
+  const title = el("h2", "", display(popNode!.id)); title.id = "pop-title"; pop.append(title);
+  const opts = el("div", "options"); variantOptions(opts, popIndex!, (j) => { popIndex = j; renderPop(); }); pop.append(opts);
+  const acts = el("div", "pop-actions");
+  const a = el("button", "b-start", "Start"), b = el("button", "b-end", "End");
+  a.type = b.type = "button";
+  a.addEventListener("click", () => setEnd("source", popIndex!)); b.addEventListener("click", () => setEnd("target", popIndex!));
+  acts.append(a, b); pop.append(acts);
+  const details = el("button", "pop-details", "Details"); details.type = "button";
+  details.onclick = () => showProblem(D.nodes[popIndex!]!); pop.append(details);
+  pop.hidden = false; placePop();
+  restoreVariantGroup(pop, focusGroup);
+}
+function placePop() {
+  if (!popNode || $("#pop").hidden) return;
+  const pop = $("#pop"), p = scene.position(popNode), r = freeRect();
+  pop.style.maxHeight = Math.max(1, r.h - 24) + "px";
+  const w = pop.offsetWidth, h = pop.offsetHeight;
+  let x = p.x + 20; if (x + w > r.x + r.w - 12) x = p.x - 20 - w;
+  pop.style.left = Math.max(r.x + 12, x) + "px";
+  pop.style.top = Math.max(r.y + 12, Math.min(p.y - h / 2, r.y + r.h - h - 12)) + "px";
+}
+function closePop(restoreFocus = false) {
+  const opener = popNode?.shape;
+  popNode = null; $("#pop").hidden = true;
+  if (restoreFocus) opener?.focus({preventScroll: true});
+}
+scene.onNodeTap = openPop;
+scene.onBackgroundTap = () => closePop();
+document.addEventListener("keydown", (e) => {
+  if (e.key === "Escape") { closePop(true); closeDetails(); }
+  if (e.key === "/" && (!modalDetails.matches || $("#details-drawer").hidden) && !document.activeElement!.matches("input, textarea, [contenteditable]")) { e.preventDefault(); $(state.source == null ? "#source" : "#target").focus(); }
+});
+
+/* ---------- On-demand articles ---------- */
+const variantKey = (variant: Endpoint['variant']) => Object.entries(variant).sort().map(([k, v]) => k + "=" + v).join(",");
+const detailId = (endpoint: Endpoint) => endpoint.name + "/" + variantKey(endpoint.variant);
+let drawerOpener: HTMLElement | SVGElement | null = null;
+const drawerBackground = new Map<HTMLElement, boolean>();
+function syncDrawerModal() {
+  const drawer = $("#details-drawer"), modal = modalDetails.matches && !drawer.hidden;
+  if (modal) {
+    drawer.setAttribute("aria-modal", "true");
+    for (const node of document.body.children) {
+      if (!(node instanceof HTMLElement) || node === drawer || drawerBackground.has(node)) continue;
+      drawerBackground.set(node, node.inert); node.inert = true;
+    }
+    if (!drawer.contains(document.activeElement)) $("#close-details").focus({preventScroll: true});
+  } else {
+    drawer.removeAttribute("aria-modal");
+    for (const [node, inert] of drawerBackground) node.inert = inert;
+    drawerBackground.clear();
+  }
+}
+function showDetails(title: string, key: string, parentKey: string) {
+  if (state.result) state.picked = true;
+  const drawer = $("#details-drawer"), body = $("#drawer-body"), atlas = $<HTMLAnchorElement>("#drawer-atlas");
+  const opening = drawer.hidden;
+  if (opening) drawerOpener = $("#pop").contains(document.activeElement) ? popNode!.shape : document.activeElement as HTMLElement | SVGElement | null;
+  closePop(); drawer.hidden = false; $(".dock").hidden = true;
+  // The drawer narrows the free canvas; reframe only when it would cover part of the selected route.
+  if (opening && !modalDetails.matches && state.result && state.selected) {
+    const r = freeRect(), b = scene.bounds(routeEls(state.selected), true);
+    if (b.x1 < r.x || b.x2 > r.x + r.w || b.y1 < r.y || b.y2 > r.y + r.h) frame(routeEls(state.selected), 1.3);
+  }
+  $("#details-title").textContent = title; body.scrollTop = 0;
+  const endpoint = (value: string) => value.split("/").map(encodeURIComponent);
+  if (key.startsWith("problem:")) {
+    const [name, variant] = endpoint(key.slice(8));
+    atlas.href = `./index.html#problem/${name}${variant ? `?variant=${variant}` : ""}`;
+  } else {
+    const [source, target] = key.slice(5).split("->").map(endpoint);
+    atlas.href = `./index.html#reduction/${source![0]}/${target![0]}?from=${source![1]}&to=${target![1]}`;
+  }
+  renderDetails(body, "", "", key, parentKey, (problem) => {
+    const [name, variant] = problem.split("/") as [string, string?];
+    const index = variant == null ? defaults[name]! : D.nodes.findIndex((n) => n.name === name && variantKey(n.variant) === variant);
+    if (index == null || index < 0) return;
+    showProblem(D.nodes[index]!); pulseAndFrame(name);
+  });
+  $("#close-details").focus({preventScroll: true}); syncDrawerModal(); scheduleLabels(); placePop();
+}
+function showProblem(endpoint: Endpoint) {
+  showDetails(display(endpoint.name), "problem:" + detailId(endpoint), "problem:" + endpoint.name);
+}
+function showRule(step: Step) {
+  showDetails(display(step.from.name) + " → " + display(step.to.name),
+    `rule:${detailId(step.from)}->${detailId(step.to)}`, `rule:${step.from.name}->${step.to.name}`);
+}
+function closeDetails() {
+  if ($("#details-drawer").hidden) return;
+  $("#details-drawer").hidden = true; $(".dock").hidden = false;
+  syncDrawerModal();
+  if (drawerOpener?.isConnected) drawerOpener.focus({preventScroll: true});
+  scheduleLabels();
+}
+function pulseAndFrame(name: string) {
+  const node = scene.byId.get(name)!; scene.classes([node], "", "pulse");
+  setTimeout(() => scene.classes([node], "pulse"), 1000); frame([node], 1.6);
+}
+$("#close-details").onclick = closeDetails;
+scene.onEdgeTap = (edge) => {
+  if (!scene.has(edge, "route")) return;
+  const step = state.result?.paths[state.selected! - 1]!.path.find((s) =>
+    s.from.name === edge.source.id && s.to.name === edge.target.id);
+  if (step) showRule(step);
+};
+modalDetails.addEventListener("change", syncDrawerModal);
+$("#details-drawer").addEventListener("keydown", (e) => {
+  if (!modalDetails.matches || e.key !== "Tab") return;
+  const items = [...$("#details-drawer").querySelectorAll<HTMLElement>('a[href], button, summary, [tabindex="0"]')].filter((n) => n.getClientRects().length);
+  const first = items[0], last = items.at(-1);
+  if (e.shiftKey && document.activeElement === first) { e.preventDefault(); last!.focus(); }
+  else if (!e.shiftKey && document.activeElement === last) { e.preventDefault(); first!.focus(); }
+});
+
+/* ---------- Path engine ---------- */
+let worker = graphStartup.worker, reqId = 0, clock = 0;
+graphStartup.worker = null;
+const cache = new Map<string, PathResult>();
+function stopWorker() { worker?.terminate(); worker = null; }
+function compute(source: number, target: number, limit: number, onPaths: (result: PathResult) => void): Promise<PathResult> {
+  const key = `${source}-${target}-${limit}`, cached = cache.get(key);
+  if (cached) {
+    cache.delete(key); cache.set(key, cached);
+    onPaths(cached);
+    if (cached.polynomial_comparison || !cached.paths.length) return Promise.resolve(cached);
+  }
+  const request: PathRequest = cached
+    ? {kind: 'compare', source, target, limit,
+      cached: {paths: cached.paths, truncated: cached.truncated}}
+    : {kind: 'search', source, target, limit};
+  return new Promise<PathResult>((resolve, reject) => {
+    try { worker ||= new Worker(new URL('../workers/path-worker.ts', import.meta.url), { type: "module" }); } catch (err) { reject(err); return; }
+    const engine = worker;
+    let result = cached;
+    worker.onmessage = ({ data }: MessageEvent<PathReply>) => {
+      if (worker !== engine) return;
+      try {
+        const started = performance.now();
+        const reply = validatePathReply(data, request, result);
+        performance.measure(`graph:${reply.phase}-validation`, {start: started});
+        performance.mark(`graph:${reply.phase}-received`);
+        if ('error' in reply) { stopWorker(); reject(new Error(reply.error)); return; }
+        if (reply.phase === "paths") {
+          result = reply.result; cache.set(key, result); onPaths(result);
+          if (cache.size > 8) cache.delete(cache.keys().next().value!);
+          if (result.paths.length) return;
+        } else {
+          result!.polynomial_comparison = reply.result;
+        }
+        resolve(result!);
+      } catch (error) {
+        stopWorker(); reject(error);
+      }
+    };
+    worker.onerror = (ev) => { ev.preventDefault(); if (worker !== engine) return; stopWorker(); reject(new Error("engine")); };
+    performance.mark("graph:request-posted");
+    worker.postMessage(request);
+  });
+}
+function orderPaths(result: PathResult) {
+  const c = result.polynomial_comparison;
+  const degrees = c?.profiles.map(pathDegree), front = new Set(c?.front);
+  result.order = result.paths.map((_, i) => i + 1).sort((a, b) =>
+    (c ? (Number(front.has(b)) - Number(front.has(a))) || compareDegrees(degrees![a - 1], degrees![b - 1]) : 0) ||
+    result.paths[a - 1]!.steps - result.paths[b - 1]!.steps || a - b);
+}
+async function run() {
+  const id = ++reqId;
+  if (state.busy) stopWorker();
+  clearInterval(clock);
+  state.result = null; state.selected = null; state.picked = false; state.showSlower = false; state.busy = true;
+  paintGraph(); renderResults();
+  frame([scene.byId.get(D.nodes[state.source!]!.name)!, scene.byId.get(D.nodes[state.target!]!.name)!], 1.1);
+  if (state.source === state.target) { state.busy = false; renderResults("same"); return; }
+  const started = Date.now();
+  clock = setInterval(() => { const s = $("#elapsed"); if (s) s.textContent = Math.round((Date.now() - started) / 1000) + " s"; }, 1000);
+  try {
+    const result = await compute(state.source!, state.target!, state.limit, (paths) => {
+      if (id !== reqId || !paths.paths.length) return;
+      orderPaths(paths); state.result = paths;
+      select(paths.order![0]!);
+      performance.mark("graph:routes-rendered");
+    });
+    if (id !== reqId) return;
+    clearInterval(clock); state.busy = false;
+    if (!result.paths.length) { renderResults("none"); paintGraph(); return; }
+    orderPaths(result); state.result = result;
+    // Until the user picks a route, show the best one; afterwards the comparison only re-ranks rows.
+    if (state.picked) { paintGraph(); renderResults(); } else select(result.order![0]!);
+    performance.mark("graph:comparison-rendered");
+  } catch (err) {
+    if (id !== reqId) return;
+    clearInterval(clock); state.busy = false; state.result = null; state.selected = null; renderResults("error"); paintGraph();
+  }
+}
+function cancel() {
+  reqId++; clearInterval(clock); stopWorker(); state.busy = false; state.result = null; state.selected = null; renderResults("cancelled"); paintGraph();
+}
+
+/* ---------- Path display ---------- */
+function endpoints(route: Route) { return [route.path[0].from, ...route.path.map((s) => s.to)]; }
+function routeEls(n: number) {
+  const ids = new Set<string>();
+  state.result!.paths[n - 1]!.path.forEach((s) => { ids.add(s.from.name); ids.add(s.to.name); if (s.from.name !== s.to.name) ids.add(s.from.name + "→" + s.to.name); });
+  return [...ids].map(id => scene.byId.get(id)!);
+}
+function paintGraph() {
+  scene.classes(scene.elements, "dim ghost route start end nbr");
+  scene.nodes.forEach(n => { n.routeLabel = display(n.id); });
+  if (state.result && state.selected) {
+    scene.classes(scene.elements, "", "dim");
+    (state.result!.polynomial_comparison?.front || []).forEach(n => scene.classes(routeEls(n), "dim", "ghost"));
+    const selected = routeEls(state.selected);
+    scene.classes(selected, "dim ghost", "route");
+    // Selected paths stay above the rest of the scene for reliable edge hit testing.
+    selected.filter(n => !n.label).forEach(n => scene.world.insertBefore(n.shape, scene.nodes[0]!.shape));
+    const labelled = new Set();
+    endpoints(state.result!.paths[state.selected! - 1]!).forEach(e => {
+      if (!multi(e.name) || labelled.has(e.name)) return;
+      labelled.add(e.name);
+      const def = D.nodes[defaults[e.name]!]!.variant;
+      const diff = Object.entries(e.variant).filter(([k,v]) => def[k] !== v).map(([k,v]) => k + ": " + v);
+      if (diff.length) (scene.byId.get(e.name)! as SceneNode).routeLabel = display(e.name) + "\n" + diff.join("  ");
+    });
+  } else if (state.source != null && state.target != null) scene.classes(scene.elements, "", "dim");
+  for (const side of ["source", "target"] as const) if (state[side] != null)
+    scene.classes([scene.byId.get(D.nodes[state[side]]!.name)!], "dim", side === "source" ? "start" : "end");
+  scene.nodes.forEach(node => node.shape.setAttribute('aria-label', scene.describe(node)));
+  scheduleLabels();
+}
+function select(n: number) {
+  state.selected = n;
+  paintGraph(); renderResults();
+  const focused = scene.nodeOf(document.activeElement);
+  if (focused) scene.reveal(focused);
+  else frame(routeEls(n), 1.3);
+}
+
+/* Problem families along a route; consecutive variants of one family are a single stop. */
+function familyChain(route: Route) {
+  const names: string[] = []; endpoints(route).forEach((e) => { if (names.at(-1) !== e.name) names.push(e.name); });
+  return names;
+}
+/* The ends are already in the search box, so a row says only what is in between; the timeline lists every stop. */
+function chain(route: Route) {
+  const names = familyChain(route), via = names.slice(1, -1);
+  const span = el("span", "chain", via.length ? `via ${display(via[0]!)}${via.length > 1 ? ` +${via.length - 1}` : ""}` : "Direct");
+  span.title = names.map(display).join(" → ");
+  return span;
+}
+function pathRow(n: number, slower: boolean) {
+  const c = state.result!.polynomial_comparison, route = state.result!.paths[n - 1]!, open = state.selected === n;
+  const wrap = el("div");
+  const b = el("button", "path" + (slower ? " slower" : "")); b.type = "button";
+  b.setAttribute("aria-expanded", String(open)); b.dataset.path = String(n);
+  const size = el("span", "size" + (c ? "" : " pending"), c ? sizeBadge(pathDegree(c.profiles[n - 1]!)) : "");
+  size.title = c && pathDegree(c.profiles[n - 1]!) == null ? "Size unavailable for one or more parameters" : "Largest growth of the reduced problem";
+  const line = el("div", "path-line"); line.append(chain(route), size);
+  b.append(line);
+  b.addEventListener("click", () => { state.picked = true; if (state.selected !== n) select(n); });
+  wrap.append(b);
+  if (open) wrap.append(pathDetail(n));
+  return wrap;
+}
+function pathDetail(n: number) {
+  const route = state.result!.paths[n - 1]!, profile = state.result!.polynomial_comparison?.profiles[n - 1]!;
+  const d = el("div", "detail");
+  const ol = el("ol", "steps");
+  // Consecutive steps inside one family are variant conversions: show the family once with each variant it passes through.
+  const groups: {name: string; variants: Endpoint['variant'][]}[] = [];
+  endpoints(route).forEach((e) => { if (groups.at(-1)?.name === e.name) groups.at(-1)!.variants.push(e.variant); else groups.push({ name: e.name, variants: [e.variant] }); });
+  groups.forEach((e, i) => {
+    const li = el("li"), btn = el("button"); btn.type = "button";
+    btn.append(el("span", "name", display(e.name)));
+    if (multi(e.name)) e.variants.forEach((v) => btn.append(kvNode(v)));
+    btn.addEventListener("click", () => { showProblem({name: e.name, variant: e.variants[0]!}); pulseAndFrame(e.name); });
+    li.append(el("span", "dot"), btn); ol.append(li);
+    if (i < groups.length - 1) {
+      const next = groups[i + 1]!, rule = el("button", "rule-link", "rule"); rule.type = "button";
+      rule.title = `Reduction rule: ${display(e.name)} to ${display(next.name)}`;
+      rule.onclick = () => showRule({from: {name: e.name, variant: e.variants.at(-1)!}, to: {name: next.name, variant: next.variants[0]!}});
+      li.append(rule);
+    }
+  });
+  const dl = el("dl", "growth");
+  Object.entries(profile?.fields || {}).forEach(([name, f]) => dl.append(el("dt", "", prettyField(name)), el("dd", "", growth(f).lead)));
+  const label = "Copy route for pred reduce --via";
+  const copy = el("button", "copy link", label); copy.type = "button";
+  copy.addEventListener("click", async () => {
+    state.picked = true;
+    const json = JSON.stringify({ steps: route.steps, path: route.path }, null, 2);
+    try { await navigator.clipboard.writeText(json); copy.textContent = "Copied"; setTimeout(() => (copy.textContent = label), 1500); }
+    catch { const t = el("textarea", "copy-text"); t.readOnly = true; t.value = json; copy.after(t); t.select(); }
+  });
+  d.append(ol);
+  if (dl.children.length) d.append(el("p", "growth-title", "Result size"), dl);
+  d.append(copy);
+  return d;
+}
+function examples() {
+  const c = el("div", "chips");
+  ([["SAT → QUBO", "Satisfiability", "QUBO"], ["MIS → QUBO", "MaximumIndependentSet", "QUBO"], ["Factoring → ILP", "Factoring", "ILP"], ["HC → QUBO", "HamiltonianCircuit", "QUBO"]] as const).forEach(([label, s, t]) => {
+    const b = el("button", "chip", label); b.type = "button";
+    b.addEventListener("click", () => { state.source = defaults[s]!; state.target = defaults[t]!; state.limit = 20; syncEnds(); run(); });
+    c.append(b);
+  });
+  return c;
+}
+function renderResults(status?: 'same' | 'none' | 'error' | 'cancelled') {
+  const box = $("#results"); box.replaceChildren();
+  if (state.source == null || state.target == null) {
+    const n = el("div", "note"); n.append(el("p", "", "Pick a start and an end problem, by searching or by clicking the graph. Try:"), examples()); box.append(n); return;
+  }
+  if (state.busy && !state.result) {
+    const s = el("div", "summary"), left = el("span", "", "Comparing paths "), t = el("span", "", ""); t.id = "elapsed"; left.append(t);
+    const c = el("button", "link", "Cancel"); c.type = "button"; c.addEventListener("click", cancel); s.append(left, c);
+    box.append(s); for (let i = 0; i < 4; i++) box.append(el("div", "skeleton")); return;
+  }
+  const msg = status && { same: "Start and end are the same problem variant.", none: "No reduction path connects these two. Try another variant of either problem.",
+    error: "Cannot load the path engine. Reload this release and try again.", cancelled: "Search cancelled." }[status];
+  if (msg) {
+    const n = el("div", "note"); n.append(el("p", "", msg));
+    if (status === "error") n.append(examples());
+    if (status === "cancelled") { const r = el("button", "link", "Search again"); r.type = "button"; r.onclick = run; n.append(r); }
+    box.append(n); return;
+  }
+  if (!state.result) return;
+  const c = state.result!.polynomial_comparison;
+  // Merge same-chain variants by rank, retaining the exact route currently selected.
+  const seen = new Set(), chainKey = (n: number) => endpoints(state.result!.paths[n - 1]!).map((e) => e.name).filter((x, i, a) => x !== a[i - 1]).join(">");
+  const selectedChain = chainKey(state.selected!);
+  const shown = state.result.order!.filter((n) => {
+    const k = chainKey(n);
+    if (seen.has(k) || (k === selectedChain && n !== state.selected)) return false;
+    seen.add(k); return true;
+  });
+  const onFront = new Set(c?.front), front = shown.filter((n) => !c || onFront.has(n)), slower = shown.filter((n) => c && !onFront.has(n));
+  const s = el("div", "summary"), left = el("span");
+  if (c) left.append(el("strong", "", `${front.length} best route${front.length === 1 ? "" : "s"}`), ` of ${shown.length}`);
+  else { const elapsed = el("span"); elapsed.id = "elapsed"; left.append("Comparing paths ", elapsed); }
+  s.append(left);
+  if (state.busy) {
+    const cancelButton = el("button", "link", "Cancel"); cancelButton.type = "button"; cancelButton.onclick = cancel; s.append(cancelButton);
+  } else if (state.result.truncated && state.limit < 999) {
+    const more = el("button", "link", "Search more"); more.type = "button";
+    more.addEventListener("click", () => { state.limit = state.limit < 50 ? 50 : state.limit < 100 ? 100 : 999; run(); });
+    s.append(more);
+  }
+  box.append(s);
+  front.forEach((n) => box.append(pathRow(n, false)));
+  if (slower.length && !front.length) slower.forEach((n) => box.append(pathRow(n, true)));
+  else if (slower.length) {
+    const open = state.showSlower || slower.includes(state.selected!);
+    const t = el("button", "link more", open ? "Hide slower routes" : `Show ${slower.length} slower routes`); t.type = "button";
+    t.addEventListener("click", () => { state.showSlower = !open; if (!state.showSlower && slower.includes(state.selected!)) { select(front[0]!); return; } renderResults(); });
+    box.append(t);
+    if (open) slower.forEach((n) => box.append(pathRow(n, true)));
+  }
+}
+
+/* ---------- Dock and resize ---------- */
+const zoomBy = (k: number) => { const r = freeRect(); scene.stop(); scene.zoomAt(scene.zoom * k, { x: r.x + r.w / 2, y: r.y + r.h / 2 }); };
+$("#zoom-in").onclick = () => zoomBy(1.3);
+$("#zoom-out").onclick = () => zoomBy(1 / 1.3);
+$("#fit").onclick = () => frame(scene.elements, 1);
+addEventListener("resize", () => { scheduleLabels(); placePop(); });
+new ResizeObserver(() => {
+  document.documentElement.style.setProperty("--header-height", $(".site-header").getBoundingClientRect().height + "px");
+  scheduleLabels();
+}).observe($(".site-header"));
+
+/* ---------- Start on a real example ---------- */
+state.source = defaults.Satisfiability!; state.target = defaults.QUBO!;
+syncEnds(); frame(scene.elements, 1, false); run();
+performance.mark("graph:interactive");
+document.fonts?.ready.then(() => {
+  scene.nodes.forEach(n => { n.labelKey = null; });
+  const focused = scene.nodes.find(node => scene.has(node, 'focused'));
+  if (focused) scene.reveal(focused);
+  scheduleLabels();
+});
+})().catch(() => {
+  graphStartup.worker?.terminate();
+  graphStartup.worker = null;
+  document.querySelector('#results')!.textContent = 'Cannot load graph. Reload this release and try again.';
+});
diff --git a/docs/website/assets/site.js b/docs/website/src/pages/site.ts
similarity index 59%
rename from docs/website/assets/site.js
rename to docs/website/src/pages/site.ts
index ab6adb0fd..7a62cd694 100644
--- a/docs/website/assets/site.js
+++ b/docs/website/src/pages/site.ts
@@ -1,9 +1,23 @@
+import { loadDetailsIndex, renderDetails } from './details.ts';
+import type { AtlasSummary, AtlasRecord, RecordEdge, SummaryEdge, Variant } from '../generated/atlas-data.mjs';
+
+declare global { interface Window { REDUCTIONS: unknown } }
+
 /* The site is a static client of the same registry exports as the book and paper. */
 (() => {
   "use strict";
-  let data = window.REDUCTIONS;
-  let fullData;
-  const main = document.querySelector("main");
+  const $ = <T extends HTMLElement = HTMLElement>(selector: string) => document.querySelector<T>(selector)!;
+  const main = $('main');
+  function showError(error: unknown) {
+    const alert = Object.assign(document.createElement('p'), {textContent: error instanceof Error ? error.message : String(error)});
+    alert.setAttribute('role', 'alert');
+    main.replaceChildren(alert);
+  }
+  const summary = window.REDUCTIONS as AtlasSummary;
+  const records = new Map<string, Promise<AtlasRecord>>();
+  const names = new Map(summary.schemas.map(schema => [schema.name, schema]));
+  let atlasRows: Map<string, Element> | undefined;
+  // The website build validates summary and record references before publishing.
   const homeHTML = main.innerHTML;
   history.scrollRestoration = "manual";
   const baseTitle = "Problem Reductions";
@@ -15,7 +29,7 @@
     algebraic: "Algebra",
     misc: "Other structures",
   };
-  const aliases = {
+  const aliases: Record<string, string> = {
     MIS: "MaximumIndependentSet",
     MVC: "MinimumVertexCover",
     SAT: "Satisfiability",
@@ -24,9 +38,9 @@
   };
   let filter = "all";
   let query = "";
-  let toastTimer;
+  let toastTimer: ReturnType<typeof setTimeout> | undefined;
   let focusSearchAfterNavigation = false;
-  const escape = (value) =>
+  const escape = (value: unknown) =>
     String(value ?? "").replace(
       /[&<>"']/g,
       (c) =>
@@ -36,51 +50,57 @@
           ">": "&gt;",
           '"': "&quot;",
           "'": "&#39;",
-        })[c],
+        } as Record<string, string>)[c]!,
     );
-  const nameOf = (name) =>
-    data.schemas.find((s) => s.name === name)?.display_name ||
+  const nameOf = (name: string) =>
+    names.get(name)?.display_name ||
     name
       .replace(/([a-z0-9])([A-Z])/g, "$1 $2")
       .replace(/([A-Z])([A-Z][a-z])/g, "$1 $2");
-  const variantKey = (node) =>
+  const variantKey = (node: {variant: Variant}) =>
     Object.entries(node.variant)
       .sort(([a], [b]) => a.localeCompare(b))
       .map(([k, v]) => `${k}=${v}`)
       .join(",");
-  const variantLabel = (node) =>
+  const variantLabel = (node: {variant: Variant}) =>
     Object.entries(node.variant)
       .map(([k, v]) => `${k}: ${v}`)
       .join(" · ") || "Default variant";
-  const problemHref = (name, node) =>
+  const problemHref = (name: string, node?: {variant: Variant}) =>
     `#problem/${encodeURIComponent(name)}${node ? `?variant=${encodeURIComponent(variantKey(node))}` : ""}`;
-  const ruleHref = (edge) =>
-    `#reduction/${encodeURIComponent(data.nodes[edge.source].name)}/${encodeURIComponent(data.nodes[edge.target].name)}?from=${encodeURIComponent(variantKey(data.nodes[edge.source]))}&to=${encodeURIComponent(variantKey(data.nodes[edge.target]))}`;
-  const schemaOf = (name) => data.schemas.find((s) => s.name === name);
-  const description = (name) =>
+  const ruleHref = (edge: SummaryEdge, nodes: AtlasSummary['nodes'] | AtlasRecord['nodes'] = summary.nodes) =>
+    `#reduction/${encodeURIComponent(nodes[edge.source]!.name)}/${encodeURIComponent(nodes[edge.target]!.name)}?from=${encodeURIComponent(variantKey(nodes[edge.source]!))}&to=${encodeURIComponent(variantKey(nodes[edge.target]!))}`;
+  const schemaOf = (name: string) => summary.schemas.find((s) => s.name === name);
+  const description = (name: string) =>
     schemaOf(name)?.description ||
     "Explore the registered variants, reduction contracts, and implementation of this computational problem.";
-  const apiHref = (path) => `./api/problemreductions/${path}`;
-  const sourceHref = (edge) => `${repo}/blob/main/${edge.source_path}`;
-  const families = [...new Set(data.nodes.map((n) => n.name))].sort();
-  const variantsOf = (name) =>
+  const apiHref = (path: string) => `./api/problemreductions/${path}`;
+  const sourceHref = (edge: RecordEdge) => `${repo}/blob/main/${edge.source_path}`;
+  const families = [...new Set(summary.nodes.map((n) => n.name))].sort();
+  const variantsOf = (name: string, data: AtlasRecord) =>
     data.nodes
       .map((n, i) => ({ ...n, index: i }))
       .filter((n) => n.name === name);
-  const edgesOf = (name) =>
-    data.edges.filter(
+  const edgesOf = (name: string) =>
+    summary.edges.filter(
       (e) =>
-        data.nodes[e.source].name === name ||
-        data.nodes[e.target].name === name,
+        summary.nodes[e.source]!.name === name ||
+        summary.nodes[e.target]!.name === name,
     );
-  const featuredEdge = data.edges.find(
+  const featuredEdge = summary.edges.find(
     (e) =>
-      data.nodes[e.source].name === "MinimumVertexCover" &&
-      data.nodes[e.target].name === "MaximumIndependentSet",
+      summary.nodes[e.source]!.name === "MinimumVertexCover" &&
+      summary.nodes[e.target]!.name === "MaximumIndependentSet",
   );
+  const catalog = families.map(name => {
+    const variants = summary.nodes.filter(node => node.name === name), category = variants[0]!.category;
+    return {name, category,
+      search: `${name} ${nameOf(name)} ${description(name)} ${(names.get(name)?.aliases || []).join(' ')}`.toLowerCase(),
+      html: `<a class="atlas-row" href="${problemHref(name)}"><div><h2>${escape(nameOf(name))}</h2><p>${escape(description(name))}</p><div class="atlas-row-meta"><span>${escape(categories[category] || category)}</span><span>${variants.length} variant${variants.length === 1 ? '' : 's'}</span><span>${edgesOf(name).length} connection${edgesOf(name).length === 1 ? '' : 's'}</span></div></div><i class="arrow ne" aria-hidden="true"></i></a>`};
+  }).sort((a, b) => nameOf(a.name).localeCompare(nameOf(b.name)));
 
-  function notify(message) {
-    const toast = document.querySelector(".toast");
+  function notify(message: string) {
+    const toast = $(".toast");
     toast.textContent = message;
     toast.classList.add("visible");
     clearTimeout(toastTimer);
@@ -90,7 +110,7 @@
   function graphArt() {
     const width = 630,
       height = 430;
-    const highlights = {
+    const highlights: Record<string, [number, number, string]> = {
       MaximumIndependentSet: [310, 242, "Independent Set"],
       MinimumVertexCover: [452, 155, "Vertex Cover"],
       Satisfiability: [145, 162, "Satisfiability"],
@@ -100,7 +120,7 @@
       ILP: [330, 370, "ILP"],
       Coloring: [92, 249, "Coloring"],
     };
-    const positions = {};
+    const positions: Record<string, [number, number, string?]> = {};
     families.forEach((name, i) => {
       const angle = i * 2.39996323;
       const radius = Math.sqrt((i + 1) / families.length);
@@ -109,17 +129,17 @@
         218 + Math.sin(angle) * radius * 191,
       ];
     });
-    const seen = new Set();
-    const lines = data.edges
+    const seen = new Set<string>();
+    const lines = summary.edges
       .map((e) => {
-        const from = data.nodes[e.source].name,
-          to = data.nodes[e.target].name;
+        const from = summary.nodes[e.source]!.name,
+          to = summary.nodes[e.target]!.name;
         if (from === to) return "";
         const key = [from, to].sort().join("/");
         if (seen.has(key)) return "";
         seen.add(key);
-        const [x1, y1] = positions[from],
-          [x2, y2] = positions[to];
+        const [x1, y1] = positions[from]!,
+          [x2, y2] = positions[to]!;
         const featured =
           [from, to].includes("MinimumVertexCover") &&
           [from, to].includes("MaximumIndependentSet");
@@ -129,7 +149,7 @@
     const nodes = [...families]
       .sort((a, b) => Number(!!highlights[a]) - Number(!!highlights[b]))
       .map((name) => {
-        const [x, y] = positions[name];
+        const [x, y] = positions[name]!;
         const isFocus = [
           "MaximumIndependentSet",
           "MinimumVertexCover",
@@ -149,12 +169,12 @@
     [200, 190],
     [100, 190],
     [69, 94],
-  ];
+  ] as const;
   function cycleSVG(mode = "independent", labels = false) {
     const selected = mode === "independent" ? [0, 2] : [1, 3, 4];
     return `<svg viewBox="0 0 300 225" role="img" aria-label="Five-vertex cycle with ${mode === "independent" ? "an independent set of two" : "a vertex cover of three"} highlighted">${cyclePoints
       .map(([x, y], i) => {
-        const next = cyclePoints[(i + 1) % cyclePoints.length];
+        const next = cyclePoints[(i + 1) % cyclePoints.length]!;
         return `<line x1="${x}" y1="${y}" x2="${next[0]}" y2="${next[1]}" stroke="var(--diagram-line)" stroke-width="1.5"/>`;
       })
       .join(
@@ -163,12 +183,12 @@
   }
 
   function complementArt() {
-    const graph = (offset, selected) =>
-      `<g transform="translate(${offset},20) scale(.67)">${cyclePoints.map(([x, y], i) => `<line x1="${x}" y1="${y}" x2="${cyclePoints[(i + 1) % 5][0]}" y2="${cyclePoints[(i + 1) % 5][1]}" stroke="var(--diagram-line)" stroke-width="2"/>`).join("")}${cyclePoints.map(([x, y], i) => `<circle cx="${x}" cy="${y}" r="13" fill="${selected.includes(i) ? "var(--diagram-selected)" : "var(--paper)"}" stroke="var(--diagram-line)" stroke-width="1.5"/>`).join("")}</g>`;
-    return `<svg viewBox="0 0 520 245" role="img" aria-label="A vertex cover of size three becomes an independent set of size two by complementing the selection">${graph(15, [1, 3, 4])}${graph(305, [0, 2])}<path d="M235 102h48m-6-6 6 6-6 6" fill="none" stroke="var(--diagram-line)" stroke-width="1.5"/><text x="260" y="133" text-anchor="middle" font-family="monospace" font-size="10" fill="var(--muted)">V ∖ S</text><g font-family="DM Sans, sans-serif" text-anchor="middle" fill="var(--diagram-label)"><text x="115" y="201" font-size="13">Minimum Vertex Cover</text><text x="405" y="201" font-size="13">Maximum Independent Set</text><text x="115" y="224" font-size="10" fill="var(--muted)">3 selected vertices</text><text x="405" y="224" font-size="10" fill="var(--muted)">2 selected vertices</text></g></svg>`;
+    const graph = (offset: number, selected: number[]) =>
+      `<g transform="translate(${offset},20) scale(.67)">${cyclePoints.map(([x, y], i) => `<line x1="${x}" y1="${y}" x2="${cyclePoints[(i + 1) % 5]![0]}" y2="${cyclePoints[(i + 1) % 5]![1]}" stroke="var(--diagram-line)" stroke-width="2"/>`).join("")}${cyclePoints.map(([x, y], i) => `<circle cx="${x}" cy="${y}" r="13" fill="${selected.includes(i) ? "var(--diagram-selected)" : "var(--paper)"}" stroke="var(--diagram-line)" stroke-width="1.5"/>`).join("")}</g>`;
+    return `<svg viewBox="0 0 520 245" role="img" aria-label="A five-cycle with a vertex cover of three filled vertices, and the two remaining vertices forming an independent set">${graph(15, [1, 3, 4])}${graph(305, [0, 2])}<path d="M232 102h54m-6-6 6 6-6 6" fill="none" stroke="var(--diagram-line)" stroke-width="1.5"/><g font-family="DM Sans, sans-serif" text-anchor="middle" fill="var(--diagram-label)"><text x="259" y="130" font-size="12" fill="var(--muted)">keep the</text><text x="259" y="145" font-size="12" fill="var(--muted)">others</text><text x="115" y="196" font-size="14" font-weight="600">Minimum Vertex Cover</text><text x="405" y="196" font-size="14" font-weight="600">Maximum Independent Set</text><text x="115" y="219" font-size="12" fill="var(--muted)">every edge touches a filled vertex</text><text x="405" y="219" font-size="12" fill="var(--muted)">no two filled vertices share an edge</text></g></svg>`;
   }
 
-  function miniArt(name) {
+  function miniArt(name: string) {
     if (name === "MaximumIndependentSet") return cycleSVG();
     if (name === "Satisfiability")
       return '<img src="./assets/sat.svg" alt="Example Boolean clauses" width="300" height="112">';
@@ -176,21 +196,21 @@
   }
 
   function hydrateHome() {
-    document.querySelector("#hero-graph").innerHTML = graphArt();
-    document.querySelector("#problem-showcase").innerHTML = [
+    $("#hero-graph").innerHTML = graphArt();
+    $("#problem-showcase").innerHTML = [
       "MaximumIndependentSet",
       "Satisfiability",
       "QUBO",
     ]
       .filter((name) => families.includes(name))
       .map((name) => {
-        const variants = variantsOf(name);
-        return `<a class="problem-card" href="${problemHref(name)}"><span class="context-label">${escape(categories[variants[0].category] || "Computational problem")}</span><h3>${escape(nameOf(name))}</h3><p>${escape(description(name))}.</p><div class="mini-art">${miniArt(name)}</div><div class="card-bottom"><span>${variants.length} variant${variants.length === 1 ? "" : "s"} · ${edgesOf(name).length} incident reductions</span><span aria-hidden="true">↗</span></div></a>`;
+        const variants = summary.nodes.filter(node => node.name === name);
+        return `<a class="problem-card" href="${problemHref(name)}"><span class="context-label">${escape(categories[variants[0]!.category] || "Computational problem")}</span><h3>${escape(nameOf(name))}</h3><p>${escape(description(name))}.</p><div class="mini-art">${miniArt(name)}</div><div class="card-bottom"><span>${variants.length} variant${variants.length === 1 ? "" : "s"} · ${edgesOf(name).length} incident reductions</span><i class="arrow ne" aria-hidden="true"></i></div></a>`;
       })
       .join("");
-    document.querySelector("#featured-art").innerHTML = complementArt();
+    $("#featured-art").innerHTML = complementArt();
     if (featuredEdge) {
-      document.querySelector("#featured-result-link").href =
+      $<HTMLAnchorElement>("#featured-result-link").href =
         ruleHref(featuredEdge);
     }
   }
@@ -207,7 +227,7 @@
       <div class="wrap atlas-layout">
         <aside class="filters" aria-label="Filter problems by category">
           <p class="context-label">Input structure</p>
-          ${[["all", "All problems"], ...Object.entries(categories)].map(([key, label]) => `<button class="filter-button" data-filter="${key}" aria-pressed="${filter === key}"><span>${label}</span><span>${key === "all" ? families.length : families.filter((name) => variantsOf(name)[0].category === key).length}</span></button>`).join("")}
+          ${[["all", "All problems"], ...Object.entries(categories)].map(([key, label]) => `<button class="filter-button" data-filter="${key}" aria-pressed="${filter === key}"><span>${label}</span><span>${key === "all" ? catalog.length : catalog.filter(entry => entry.category === key).length}</span></button>`).join("")}
         </aside>
         <div class="atlas-catalog">
           <div class="atlas-controls">
@@ -227,82 +247,73 @@
               /><kbd>/</kbd></label
             ><span class="result-count" role="status" aria-live="polite"></span>
             <a class="text-link" href="./graph.html"
-              >Explore the reduction graph <span aria-hidden="true">↗</span></a
+              >Explore the reduction graph <i class="arrow ne" aria-hidden="true"></i></a
             >
           </div>
           <div class="atlas-results" id="atlas-results"></div>
         </div>
       </div>`;
     renderResults();
-    document
-      .querySelector("#atlas-search")
+    $("#atlas-search")
       .addEventListener("input", (event) => {
-        query = event.target.value;
+        query = (event.currentTarget as HTMLInputElement).value;
         renderResults();
       });
-    document.querySelectorAll("[data-filter]").forEach((button) =>
+    document.querySelectorAll<HTMLElement>("[data-filter]").forEach((button) =>
       button.addEventListener("click", () => {
-        filter = button.dataset.filter;
+        filter = button.dataset.filter!;
         document
-          .querySelectorAll("[data-filter]")
-          .forEach((b) => b.setAttribute("aria-pressed", b === button));
+          .querySelectorAll<HTMLElement>("[data-filter]")
+          .forEach((b) => b.setAttribute("aria-pressed", String(b === button)));
         renderResults();
       }),
     );
   }
 
   function renderResults() {
+    if (!atlasRows) {
+      const rows = document.createElement('div');
+      rows.innerHTML = catalog.map(entry => entry.html).join('');
+      atlasRows = new Map(catalog.map((entry, i) => [entry.name, rows.children[i]!]));
+    }
     const search = query.trim().toLowerCase();
     const alias = aliases[query.trim().toUpperCase()] || "";
-    const results = families.filter((name) => {
-      const schema = schemaOf(name);
-      return (
-        (filter === "all" || variantsOf(name)[0].category === filter) &&
-        (!search ||
-          name === alias ||
-          `${name} ${nameOf(name)} ${description(name)} ${(schema?.aliases || []).join(" ")}`
-            .toLowerCase()
-            .includes(search))
-      );
-    }).sort((a, b) => nameOf(a).localeCompare(nameOf(b)));
-    document.querySelector(".result-count").textContent =
+    const results = catalog.filter(entry =>
+      (filter === 'all' || entry.category === filter) &&
+      (!search || entry.name === alias || entry.search.includes(search)));
+    $(".result-count").textContent =
       `${results.length} problem${results.length === 1 ? "" : "s"}`;
-    document.querySelector("#atlas-results").innerHTML = results.length
-      ? results
-          .map((name) => {
-            const variants = variantsOf(name);
-            return `<a class="atlas-row" href="${problemHref(name)}"><div><h2>${escape(nameOf(name))}</h2><p>${escape(description(name))}</p><div class="atlas-row-meta"><span>${escape(categories[variants[0].category] || variants[0].category)}</span><span>${variants.length} variant${variants.length === 1 ? "" : "s"}</span><span>${edgesOf(name).length} connections</span></div></div><span aria-hidden="true">↗</span></a>`;
-          })
-          .join("")
-      : `<div class="empty-state"><h2>No matching problems.</h2><p>Try a broader term or explore another input structure.</p><button class="button secondary" id="reset-search">Reset search and filters</button></div>`;
-    document.querySelector("#reset-search")?.addEventListener("click", () => {
+    const box = $('#atlas-results');
+    if (results.length) box.replaceChildren(...results.map(entry => atlasRows!.get(entry.name)!));
+    else box.innerHTML = `<div class="empty-state"><h2>No matching problems.</h2><p>Try a broader term or explore another input structure.</p><button class="button secondary" id="reset-search">Reset search and filters</button></div>`;
+    $("#reset-search")?.addEventListener("click", () => {
       query = "";
       filter = "all";
       atlasPage();
-      document.querySelector("#atlas-search").focus();
+      $("#atlas-search").focus();
     });
   }
 
-  function relation(edge, currentIndex) {
-    const source = data.nodes[edge.source],
-      target = data.nodes[edge.target];
+  function relation(edge: RecordEdge, currentIndex: number, data: AtlasRecord) {
+    const source = data.nodes[edge.source]!,
+      target = data.nodes[edge.target]!;
     const outgoing = edge.source === currentIndex;
     const other = outgoing ? target : source;
     const variant = Object.keys(other.variant).length ? variantLabel(other) : "";
-    return `<a class="relation-link" href="${ruleHref(edge)}"><div class="relation-main"><div class="relation-title"><span>${outgoing ? "→ " : ""}${escape(nameOf(other.name))}${outgoing ? "" : " →"}</span></div>${variant ? `<p>${escape(variant)}</p>` : ""}</div>${edge.turing ? '<span class="capability">Turing reduction</span>' : ""}</a>`;
+    return `<a class="relation-link" href="${ruleHref(edge, data.nodes)}"><div class="relation-main"><div class="relation-title"><span>${outgoing ? "→ " : ""}${escape(nameOf(other.name))}${outgoing ? "" : " →"}</span></div>${variant ? `<p>${escape(variant)}</p>` : ""}</div>${edge.turing ? '<span class="capability">Turing reduction</span>' : ""}</a>`;
   }
 
-  function codePanel(command) {
+  function codePanel(command: string) {
     return `<div class="code-panel"><div class="terminal-header"><button class="copy-button" data-copy="${escape(command)}" aria-label="Copy command">Copy</button></div><pre>${escape(command)}</pre></div>`;
   }
 
-  function openReferenceProblem(key) {
-    const [name, variant] = key.split("/");
+  function openReferenceProblem(key: string) {
+    const [name, variant] = key.split("/") as [string, string?];
     location.hash = `#problem/${encodeURIComponent(name)}${variant ? `?variant=${encodeURIComponent(variant)}` : ""}`;
   }
 
-  function problemPage(name, params) {
-    const variants = variantsOf(name);
+  function problemPage(name: string, params: URLSearchParams, data: AtlasRecord) {
+    const variants = variantsOf(name, data);
     if (!variants.length) return notFound();
     const requested = params.get("variant");
     if (
@@ -315,14 +326,14 @@
       variants.find(
         (n) => n.variant.graph === "SimpleGraph" && n.variant.weight === "One",
       ) ||
-      variants[0];
-    const schema = schemaOf(name);
+      variants[0]!;
+    const schema = data.schemas[0];
     const incoming = data.edges.filter((e) => e.target === node.index);
     const outgoing = data.edges.filter((e) => e.source === node.index);
     document.title = `${nameOf(name)} — ${baseTitle}`;
     main.innerHTML = /* HTML */ `<div class="wrap page-header detail-header">
         <div class="breadcrumbs">
-          <a href="#atlas">← Back</a>
+          <a href="#atlas"><i class="arrow w" aria-hidden="true"></i> Back</a>
         </div>
         <h1>${escape(nameOf(name))}</h1>
         <div class="variant-control">
@@ -334,7 +345,7 @@
       </div>
       <div class="wrap reading-layout">
         <div class="reading-content">
-          <div class="reference-tools" aria-label="Problem tools">
+          <div class="reference-tools" role="group" aria-label="Problem tools">
             <button aria-expanded="false" aria-controls="problem-connections">Connections <span>${incoming.length + outgoing.length}</span></button>
             <button aria-expanded="false" aria-controls="problem-fields">Instance fields <span>${schema?.fields?.length || 0}</span></button>
             <button aria-expanded="false" aria-controls="problem-commands">CLI commands</button>
@@ -342,11 +353,11 @@
           <section id="problem-connections" class="reference-tool-panel" aria-label="Connections" hidden>
             <section class="connection-group" aria-label="Incoming reductions">
               <header><h3>Incoming <span>${incoming.length}</span></h3><span>Other problems → ${escape(nameOf(name))}</span></header>
-              ${incoming.map((e) => relation(e, node.index)).join("")}
+              ${incoming.map((e) => relation(e, node.index, data)).join("")}
             </section>
             <section class="connection-group" aria-label="Outgoing reductions">
               <header><h3>Outgoing <span>${outgoing.length}</span></h3><span>${escape(nameOf(name))} → Other problems</span></header>
-              ${outgoing.map((e) => relation(e, node.index)).join("")}
+              ${outgoing.map((e) => relation(e, node.index, data)).join("")}
             </section>
           </section>
           <section id="problem-fields" class="reference-tool-panel" aria-label="Instance fields" hidden>
@@ -378,52 +389,51 @@
               <dd>${incoming.length} incoming · ${outgoing.length} outgoing</dd>
             </div>
           </dl>
-          <a href="${repo}/blob/main/${schema.source_path}">Open implementation <span>↗</span></a>
+          <a href="${repo}/blob/main/${schema.source_path}">Open implementation <i class="arrow ne" aria-hidden="true"></i></a>
           <a href="${escape(apiHref(node.api_path))}"
-            >Open API reference <span>↗</span></a
-          ><a href="./reductions.pdf">Open PDF reference <span>↗</span></a
-          ><a href="#atlas">Back to the atlas <span>←</span></a>
+            >Open API reference <i class="arrow ne" aria-hidden="true"></i></a
+          ><a href="./reductions.pdf">Open PDF reference <i class="arrow ne" aria-hidden="true"></i></a
+          ><a href="#atlas">Back to the atlas <i class="arrow w" aria-hidden="true"></i></a>
           <p>
             Generated from the library registry. Complexity expressions describe
             registered worst-case bounds; see the cited algorithms in the paper.
           </p>
         </aside>
       </div>`;
-    document
-      .querySelector("#variant-select")
+    $("#variant-select")
       .addEventListener("change", (event) => {
         const selected = variants.find(
-          (n) => variantKey(n) === event.target.value,
+          (n) => variantKey(n) === (event.currentTarget as HTMLSelectElement).value,
         );
         location.hash = problemHref(name, selected);
       });
-    window.renderDetails(document.querySelector("#reference-detail"), "", "",
+    renderDetails($("#reference-detail"), "", "",
       `problem:${name}/${variantKey(node)}`, `problem:${name}`, openReferenceProblem);
   }
 
-  function rulePage(sourceName, targetName, params) {
+  function rulePage(sourceName: string, targetName: string | undefined, params: URLSearchParams, data: AtlasRecord) {
     const edge = data.edges.find(
       (e) =>
-        data.nodes[e.source].name === sourceName &&
-        data.nodes[e.target].name === targetName &&
-        (!params.has("from") || variantKey(data.nodes[e.source]) === params.get("from")) &&
-        (!params.has("to") || variantKey(data.nodes[e.target]) === params.get("to")),
+        data.nodes[e.source]!.name === sourceName &&
+        data.nodes[e.target]!.name === targetName &&
+        (!params.has("from") || variantKey(data.nodes[e.source]!) === params.get("from")) &&
+        (!params.has("to") || variantKey(data.nodes[e.target]!) === params.get("to")),
     );
     if (!edge) return notFound();
-    const source = data.nodes[edge.source],
-      target = data.nodes[edge.target];
-    document.title = `${nameOf(sourceName)} → ${nameOf(targetName)} — ${baseTitle}`;
+    const source = data.nodes[edge.source]!,
+      target = data.nodes[edge.target]!;
+    document.title = `${nameOf(sourceName)} → ${nameOf(target.name)} — ${baseTitle}`;
     main.innerHTML = /* HTML */ `<div class="wrap page-header detail-header">
         <div class="breadcrumbs">
-          <a href="#atlas">← Back</a>
+          <a href="#atlas"><i class="arrow w" aria-hidden="true"></i> Back</a>
         </div>
-        <h1>${escape(nameOf(sourceName))} → ${escape(nameOf(targetName))}</h1>
+        <h1>${escape(nameOf(sourceName))} → ${escape(nameOf(target.name))}</h1>
       </div>
       <div class="wrap reading-layout">
         <div class="reading-content">
           <dl class="rule-endpoints">
-            <div><dt>Source</dt><dd class="rule-endpoint"><a href="${problemHref(sourceName, source)}">${escape(nameOf(sourceName))} <span aria-hidden="true">↗</span></a>${Object.keys(source.variant).length ? `<span>${escape(variantLabel(source))}</span>` : ""}</dd></div>
-            <div><dt>Target</dt><dd class="rule-endpoint"><a href="${problemHref(targetName, target)}">${escape(nameOf(targetName))} <span aria-hidden="true">↗</span></a>${Object.keys(target.variant).length ? `<span>${escape(variantLabel(target))}</span>` : ""}</dd></div>
+            <div><dt>Source</dt><dd class="rule-endpoint"><a href="${problemHref(sourceName, source)}">${escape(nameOf(sourceName))} <i class="arrow ne" aria-hidden="true"></i></a>${Object.keys(source.variant).length ? `<span>${escape(variantLabel(source))}</span>` : ""}</dd></div>
+            <div><dt>Target</dt><dd class="rule-endpoint"><a href="${problemHref(target.name, target)}">${escape(nameOf(target.name))} <i class="arrow ne" aria-hidden="true"></i></a>${Object.keys(target.variant).length ? `<span>${escape(variantLabel(target))}</span>` : ""}</dd></div>
           </dl>
           <section id="rule-parameters" aria-label="Parameters">
             <h2>Parameters</h2>
@@ -433,14 +443,14 @@
         </div>
         <aside class="reading-aside">
           ${edge.turing ? '<p class="rule-kind">Turing reduction</p>' : ""}
-          <a href="${sourceHref(edge)}">Open implementation <span>↗</span></a
+          <a href="${sourceHref(edge)}">Open implementation <i class="arrow ne" aria-hidden="true"></i></a
           ><a href="${escape(apiHref(edge.api_path))}"
-            >Open API reference <span>↗</span></a
-          ><a href="./reductions.pdf">Open PDF reference <span>↗</span></a>
-          <a href="${repo}/${edge.test_path ? "blob/main/" + edge.test_path : "tree/main/src/unit_tests/rules"}">Test source <span>↗</span></a>
+            >Open API reference <i class="arrow ne" aria-hidden="true"></i></a
+          ><a href="./reductions.pdf">Open PDF reference <i class="arrow ne" aria-hidden="true"></i></a>
+          <a href="${repo}/${edge.test_path ? "blob/main/" + edge.test_path : "tree/main/src/unit_tests/rules"}">Test source <i class="arrow ne" aria-hidden="true"></i></a>
         </aside>
       </div>`;
-    window.renderDetails(document.querySelector("#reference-detail"), "", "",
+    renderDetails($("#reference-detail"), "", "",
       `rule:${sourceName}/${variantKey(source)}->${targetName}/${variantKey(target)}`,
       `rule:${sourceName}->${targetName}`, openReferenceProblem);
   }
@@ -453,27 +463,32 @@
 
   async function render() {
     const hash = location.hash.slice(1) || "home";
-    const [path, search = ""] = hash.split("?");
-    let parts;
+    const [path, search = ""] = hash.split("?") as [string, string?];
+    let parts: [string, ...string[]];
     try {
-      parts = path.split("/").map(decodeURIComponent);
+      parts = path.split("/").map(decodeURIComponent) as [string, ...string[]];
     } catch {
       notFound();
       return;
     }
     const params = new URLSearchParams(search);
-    if (["atlas", "problem", "reduction"].includes(parts[0])) {
+    let record: AtlasRecord | undefined;
+    if (["atlas", "problem", "reduction"].includes(parts[0])) loadDetailsIndex().catch(() => {});
+    if (["problem", "reduction"].includes(parts[0])) {
+      const name = parts[1];
+      if (!name || !families.includes(name)) { notFound(); return; }
       try {
-        fullData ||= fetch("./assets/atlas-data.json").then(response => {
-          if (!response.ok) throw new Error("Cannot load atlas. Reload the page to get the current release.");
-          return response.json();
-        });
-        data = await fullData;
+        if (!records.has(name)) {
+          records.set(name, fetch(`./assets/problem-data/${encodeURIComponent(name)}.json`).then(response => {
+            if (!response.ok) throw new Error("Cannot load atlas. Reload the page to get the current release.");
+            return response.json() as Promise<AtlasRecord>;
+          }));
+        }
+        record = await records.get(name)!;
         if ((location.hash.slice(1) || "home") !== hash) return;
       } catch (error) {
-        fullData = null;
-        main.replaceChildren(Object.assign(document.createElement("p"), {textContent: error.message}));
-        main.firstChild.setAttribute("role", "alert");
+        records.delete(name);
+        showError(error);
         return;
       }
     }
@@ -494,10 +509,10 @@
       location.replace("./open-questions/");
       return;
     }
-    else if (parts[0] === "problem") problemPage(parts[1], params);
-    else if (parts[0] === "reduction") rulePage(parts[1], parts[2], params);
+    else if (parts[0] === "problem") problemPage(parts[1]!, params, record!);
+    else if (parts[0] === "reduction") rulePage(parts[1]!, parts[2], params, record!);
     else notFound();
-    document.querySelectorAll("[data-nav]").forEach((link) => {
+    document.querySelectorAll<HTMLElement>("[data-nav]").forEach((link) => {
       const active =
         link.dataset.nav === parts[0] ||
         (["problem", "reduction"].includes(parts[0]) &&
@@ -518,12 +533,13 @@
     if (location.hash !== "#atlas") {
       focusSearchAfterNavigation = true;
       location.hash = "atlas";
-    } else document.querySelector("#atlas-search")?.focus();
+    } else $("#atlas-search")?.focus();
   }
   document.addEventListener("keydown", (event) => {
+    const target = event.target as HTMLElement;
     const typing =
-      /INPUT|TEXTAREA|SELECT/.test(event.target.tagName) ||
-      event.target.isContentEditable;
+      /INPUT|TEXTAREA|SELECT/.test(target.tagName) ||
+      target.isContentEditable;
     if (
       ((event.metaKey || event.ctrlKey) && event.key.toLowerCase() === "k") ||
       (event.key === "/" && !typing)
@@ -533,20 +549,21 @@
     }
   });
   document.addEventListener("click", async (event) => {
+    if (!(event.target instanceof Element)) return;
     const tool = event.target.closest('.reference-tools button');
     if (tool) {
       const open = tool.getAttribute('aria-expanded') === 'false';
-      tool.parentElement.querySelectorAll('button').forEach((button) => {
+      tool.parentElement!.querySelectorAll('button').forEach((button) => {
         const selected = button === tool && open;
         button.setAttribute('aria-expanded', String(selected));
-        document.getElementById(button.getAttribute('aria-controls')).hidden = !selected;
+        document.getElementById(button.getAttribute('aria-controls')!)!.hidden = !selected;
       });
       return;
     }
-    const button = event.target.closest("[data-copy]");
+    const button = event.target.closest<HTMLElement>("[data-copy]");
     if (!button) return;
     try {
-      await navigator.clipboard.writeText(button.dataset.copy);
+      await navigator.clipboard.writeText(button.dataset.copy!);
       notify("Command copied to clipboard");
     } catch {
       notify("Select the command to copy it. Clipboard access is unavailable.");
@@ -555,7 +572,7 @@
   window.addEventListener("hashchange", async () => {
     await render();
     if (focusSearchAfterNavigation) {
-      document.querySelector("#atlas-search")?.focus();
+      $("#atlas-search")?.focus();
       focusSearchAfterNavigation = false;
     } else {
       main.focus({ preventScroll: true });
diff --git a/docs/website/assets/details.css b/docs/website/src/styles/details.css
similarity index 88%
rename from docs/website/assets/details.css
rename to docs/website/src/styles/details.css
index 50b796423..34cb0957f 100644
--- a/docs/website/assets/details.css
+++ b/docs/website/src/styles/details.css
@@ -6,10 +6,10 @@
 .typst-math > svg { display: inline-block !important; vertical-align: baseline; }
 div.typst-math { overflow-x: auto; margin: 14px 0; }
 .typst-detail figure { margin: 20px 0; }
-.typst-detail figure > svg { filter: none; background: #eef3e8; border-radius: 4px; padding: 16px; box-sizing: border-box; width: min(100%, 260px) !important; height: auto !important; margin-inline: auto; }
+.typst-detail figure > svg { filter: none; background: #eef3e8; border-radius: 8px; padding: 16px; box-sizing: border-box; width: min(100%, 260px) !important; height: auto !important; margin-inline: auto; }
 .typst-detail figcaption { color: #a9b5a4; font-size: 13px; margin-top: 10px; }
 .typst-detail figcaption svg { filter: invert(.9); }
-.typst-detail pre { overflow: auto; max-height: 240px; padding: 12px; border: 1px solid var(--line); border-radius: 4px; font-size: 14px; line-height: 1.7; }
+.typst-detail pre { overflow: auto; max-height: 240px; padding: 12px; border: 1px solid var(--line); border-radius: 8px; font-size: 14px; line-height: 1.7; }
 :is(.graph-detail, .reference-detail) a { color: #c4dda6; text-decoration: underline; text-underline-offset: 3px; overflow-wrap: anywhere; }
 .detail-references { margin-top: 26px; border-top: 1px solid var(--line); padding-top: 14px; font-size: 13px; }
 .detail-references summary { cursor: pointer; }
@@ -18,7 +18,7 @@ div.typst-math { overflow-x: auto; margin: 14px 0; }
 .detail-references li { margin: 14px 0; overflow-wrap: anywhere; }
 .detail-pdf { display: inline-block; margin-top: 24px; font-size: 14px; }
 
-.graph-detail .detail-atlas { display: inline-flex; font-size: 14px; margin-bottom: 10px; padding: 7px 12px; border: 1px solid var(--line); border-radius: 4px; text-decoration: none; }
+.graph-detail .detail-atlas { display: inline-flex; font-size: 14px; margin-bottom: 10px; padding: 7px 12px; border: 1px solid var(--line); border-radius: 8px; text-decoration: none; }
 .graph-detail .detail-atlas:hover { background: var(--pale); }
 .reference-detail { min-width: 0; padding-block: 12px 36px; border-top: 0; }
 .reference-detail:has(.detail-references) { padding-bottom: 0; }
@@ -28,8 +28,8 @@ div.typst-math { overflow-x: auto; margin: 14px 0; }
 .reference-detail .detail-references[open] { padding-bottom: 24px; }
 .reference-detail > .detail-source { margin: 0 0 24px; font-size: 13px; }
 .reference-detail .typst-detail { font-size: 16px; line-height: 1.9; }
-.reference-detail .typst-detail h3 { font-size: 19px; margin: 36px 0 14px; }
-.reference-detail .typst-detail h3:first-of-type { margin-top: 0; }
+.reference-detail .typst-detail h2 { font-size: 19px; margin: 36px 0 14px; font-weight: 600; letter-spacing: -.025em; line-height: 1.3; }
+.reference-detail .typst-detail h2:first-of-type { margin-top: 0; }
 .reference-detail .typst-detail p { margin: 14px 0; }
 .reference-detail .typst-detail figure { margin: 32px 0; }
 .reference-detail .typst-detail figure > svg { display: block; width: min(100%, 420px) !important; padding: 24px; }
diff --git a/docs/website/src/styles/graph.css b/docs/website/src/styles/graph.css
new file mode 100644
index 000000000..e61765559
--- /dev/null
+++ b/docs/website/src/styles/graph.css
@@ -0,0 +1,197 @@
+@font-face {
+  font-family: "DM Mono";
+  src: url("../../assets/fonts/dm-mono-regular.woff2") format("woff2");
+  font-weight: 400;
+  font-style: normal;
+  font-display: swap;
+}
+@font-face {
+  font-family: "DM Mono";
+  src: url("../../assets/fonts/dm-mono-medium.woff2") format("woff2");
+  font-weight: 500;
+  font-style: normal;
+  font-display: swap;
+}
+@font-face {
+  font-family: "Instrument Serif";
+  src: url("../../assets/fonts/instrument-serif-italic.woff2") format("woff2");
+  font-weight: 400;
+  font-style: italic;
+  font-display: swap;
+}
+/* Layout: the graph is the page; one translucent path panel floats at left
+   (bottom sheet on phones); a small popover appears beside a clicked node. */
+:root {
+  color-scheme: dark;
+  --bg: #0b110d;
+  --panel: rgba(18, 27, 21, .88);
+  --raised: #17221b;
+  --hover: rgba(237, 242, 232, .06);
+  --line: rgba(237, 242, 232, .08);
+  --ink: #eef3e9;
+  --ink-2: #a5b3a7;
+  --ink-3: #6b796e;
+  --accent: #cfe8a0;
+  --accent-ink: #13200f;
+  --start: #8fd3d6;
+  --end: #f0b77f;
+  --display: "Instrument Serif", Georgia, serif;
+  --sans: "DM Sans", system-ui, -apple-system, "Segoe UI", sans-serif;
+  --mono: "DM Mono", ui-monospace, SFMono-Regular, Menlo, monospace;
+  --header-height: 85px;
+}
+* { box-sizing: border-box; }
+html, body { height: 100%; }
+body { margin: 0; overflow: hidden; background: var(--bg); color: var(--ink); font: 14px/1.45 var(--sans); -webkit-font-smoothing: antialiased; }
+button, input { font: inherit; color: inherit; }
+button { cursor: pointer; background: none; border: 0; padding: 0; }
+:focus-visible { outline: 2px solid var(--accent); outline-offset: 2px; border-radius: 6px; }
+
+#canvas { position: fixed; inset: 0; background:
+  radial-gradient(ellipse at 62% 48%, transparent 35%, rgba(0,0,0,.4)),
+  radial-gradient(circle at 1px 1px, rgba(237,242,232,.045) 1px, transparent 0) 0 0 / 24px 24px; }
+#cy { position: absolute; inset: 0; }
+.graph-scene { width: 100%; height: 100%; touch-action: none; user-select: none; }
+.scene-edge { stroke: var(--ink); stroke-width: .7; opacity: .09; pointer-events: none; }
+.scene-edge.dim { opacity: .025; }
+.scene-edge.nbr { stroke: var(--ink-2); opacity: .45; }
+.scene-edge.ghost { stroke: var(--accent); stroke-width: 1.5; opacity: .22; }
+.scene-edge.route { stroke: var(--accent); stroke-width: 1.8; opacity: 1; marker-end: url(#route-arrow); pointer-events: stroke; cursor: pointer; }
+.scene-node { cursor: pointer; }
+.node-disc { stroke: var(--bg); stroke-width: 2; }
+.node-halo { fill: var(--ink); opacity: 0; }
+.node-label { font-family: var(--sans); font-weight: 500; fill: var(--ink-2); stroke: var(--bg); stroke-width: 5;
+  paint-order: stroke; stroke-linejoin: round; visibility: hidden; pointer-events: none; }
+.scene-node.named .node-label, .scene-node:is(.route,.start,.end,.hover,.focused) .node-label { visibility: visible; }
+.scene-node.dim { opacity: .16; }
+.scene-node.ghost { opacity: .75; }
+.scene-node:is(.route,.start,.end,.hover,.focused) { opacity: 1; }
+.scene-node:is(.route,.start,.end,.hover,.focused) .node-label { fill: var(--ink); }
+.scene-node.route .node-disc { stroke: var(--accent); }
+.scene-node.start .node-disc { stroke: var(--start); stroke-width: 3; }
+.scene-node.end .node-disc { stroke: var(--end); stroke-width: 3; }
+.scene-node.hover .node-halo { opacity: .12; }
+.scene-node.start .node-halo { fill: var(--start); opacity: .22; }
+.scene-node.end .node-halo { fill: var(--end); opacity: .22; }
+.scene-node.pulse .node-halo { fill: var(--accent); opacity: .4; r: 20; }
+
+/* Panel */
+.site-header { z-index: 4; }
+.panel { position: fixed; z-index: 3; left: 16px; top: calc(var(--header-height) + 16px); bottom: 16px; width: 360px;
+  display: flex; flex-direction: column; background: var(--panel); border: 1px solid var(--line);
+  border-radius: 18px; box-shadow: 0 24px 60px rgba(0,0,0,.45);
+  backdrop-filter: blur(16px) saturate(1.1); -webkit-backdrop-filter: blur(16px) saturate(1.1); }
+.panel-head { padding: 18px 20px 6px; }
+.brand { margin: 0; font: 600 15px/1.2 var(--sans); color: var(--ink); }
+
+.ends { position: relative; padding: 10px 12px 14px; border-bottom: 1px solid var(--line); }
+.end { position: relative; display: grid; grid-template-columns: 22px 1fr; align-items: start; padding: 4px 44px 4px 8px; border-radius: 12px; }
+.end:focus-within { background: var(--hover); }
+.end .pin { margin-top: 13px; width: 9px; height: 9px; border-radius: 50%; background: var(--start); box-shadow: 0 0 0 4px color-mix(in oklab, var(--start) 18%, transparent); }
+.end.to .pin { background: var(--end); box-shadow: 0 0 0 4px color-mix(in oklab, var(--end) 18%, transparent); }
+.end input { width: 100%; height: 34px; padding: 0; border: 0; background: transparent; font-size: 16px; font-weight: 500; outline: none; text-overflow: ellipsis; }
+.end input::placeholder { color: var(--ink-2); font-weight: 400; }
+.swap { position: absolute; right: 18px; top: 38px; width: 30px; height: 30px; border-radius: 50%; color: var(--ink-3); display: grid; place-items: center; }
+.swap:hover { color: var(--ink); background: var(--hover); }
+.options { display: grid; gap: 6px; padding: 2px 0 8px; }
+.opt-row { display: flex; align-items: center; flex-wrap: wrap; gap: 4px; }
+.opt-key { font: 12px var(--mono); color: var(--ink-2); margin-right: 4px; }
+.opt { font: 12px var(--mono); padding: 3px 8px; border-radius: 999px; color: var(--ink-2); border: 1px solid var(--line); }
+.opt:hover { color: var(--ink); border-color: rgba(237,242,232,.2); }
+.opt[aria-pressed="true"] { background: var(--ink); color: var(--bg); border-color: var(--ink); }
+
+.suggest { position: absolute; z-index: 5; left: 12px; right: 12px; padding: 6px; background: var(--raised); border: 1px solid var(--line); border-radius: 14px; box-shadow: 0 18px 40px rgba(0,0,0,.5); }
+.suggest button { display: flex; width: 100%; align-items: baseline; gap: 8px; padding: 8px 10px; border-radius: 9px; text-align: left; }
+.suggest button[aria-selected="true"] { background: var(--hover); }
+.suggest small { color: var(--ink-2); font: 12px var(--mono); margin-left: auto; }
+
+/* Results */
+.results { flex: 1; min-height: 0; overflow-y: auto; padding: 14px 12px 16px; overscroll-behavior: contain; scrollbar-width: thin; }
+.summary { display: flex; align-items: baseline; justify-content: space-between; padding: 0 10px 8px; color: var(--ink-2); font-size: 13px; }
+.summary strong { color: var(--ink); font-weight: 600; font-size: 14px; }
+.link { color: var(--ink-2); font-size: 13px; text-decoration: underline; text-decoration-color: var(--ink-3); text-underline-offset: 3px; }
+.link:hover { color: var(--ink); }
+.path { display: block; width: 100%; text-align: left; padding: 10px; border-radius: 12px; }
+.path:hover { background: var(--hover); }
+.path[aria-expanded="true"] { background: color-mix(in oklab, var(--accent) 8%, transparent); border-radius: 12px 12px 0 0; }
+.path-line { display: flex; align-items: center; gap: 10px; }
+.chain { flex: 1; min-width: 0; white-space: nowrap; overflow: hidden; text-overflow: ellipsis; font-size: 14px; color: var(--ink); }
+.size { flex: none; font: 500 12px var(--mono); padding: 2px 8px; border-radius: 999px; background: rgba(237,242,232,.08); color: var(--ink-2); }
+.path[aria-expanded="true"] .size { background: var(--accent); color: var(--accent-ink); }
+.slower .chain { color: var(--ink-2); }
+
+.detail { padding: 2px 12px 14px; background: color-mix(in oklab, var(--accent) 8%, transparent); border-radius: 0 0 12px 12px; }
+.steps { list-style: none; margin: 0 0 12px; padding: 0; }
+.steps li { position: relative; display: grid; grid-template-columns: 18px 1fr auto; gap: 6px; padding: 5px 0; }
+.steps li::before { content: ""; position: absolute; left: 4px; top: 19px; bottom: -7px; width: 2px; background: rgba(237,242,232,.18); }
+.steps li:last-child::before { display: none; }
+.steps .dot { margin-top: 6px; width: 9px; height: 9px; border-radius: 50%; border: 1.5px solid var(--ink-3); background: var(--bg); }
+.steps li:first-child .dot { background: var(--start); border-color: var(--start); }
+.steps li:last-child .dot { background: var(--end); border-color: var(--end); }
+.steps button { text-align: left; }
+.steps .name { font-size: 14px; }
+.steps button:hover .name { text-decoration: underline; text-underline-offset: 3px; text-decoration-color: var(--ink-3); }
+.kv { display: block; position: relative; font: 12px var(--mono); color: var(--ink); }
+.kv i { font-style: normal; color: var(--ink-2); }
+.kv + .kv::before { content: "↓ "; position: absolute; left: -14px; color: var(--ink-3); }
+.growth-title { margin: 0 0 6px; font-size: 12px; color: var(--ink-3); }
+.growth { display: grid; grid-template-columns: auto 1fr; gap: 4px 12px; margin: 0 0 12px; font-size: 13px; }
+.growth dt { color: var(--ink-2); }
+.growth dd { margin: 0; font: 12.5px/1.5 var(--mono); color: var(--ink); overflow-wrap: anywhere; }
+.copy { color: var(--ink-2); font-size: 13px; }
+.copy:hover { color: var(--ink); }
+.copy-text { display: block; width: 100%; height: 120px; margin-top: 8px; padding: 8px; font: 12px var(--mono); background: rgba(0,0,0,.25); color: var(--ink); border: 1px solid var(--line); border-radius: 10px; }
+.more { display: block; margin: 10px 10px 4px; }
+.note { padding: 2px 10px; color: var(--ink-2); font-size: 13px; }
+.note p { margin: 0 0 10px; }
+.chips { display: flex; flex-wrap: wrap; gap: 6px; }
+.chip { padding: 6px 11px; border-radius: 999px; border: 1px solid var(--line); color: var(--ink); font-size: 13px; }
+.chip:hover { background: var(--hover); }
+.skeleton { height: 40px; margin: 4px 0; border-radius: 12px; background: linear-gradient(90deg, rgba(237,242,232,.04), rgba(237,242,232,.08), rgba(237,242,232,.04)) 0 0 / 200% 100%; animation: shimmer 1.4s linear infinite; }
+@keyframes shimmer { to { background-position: -200% 0; } }
+
+/* Popover */
+.pop { position: fixed; z-index: 4; width: 250px; padding: 14px; overflow-y: auto; background: var(--raised); border: 1px solid var(--line); border-radius: 14px; box-shadow: 0 18px 44px rgba(0,0,0,.55); }
+.pop h2 { margin: 0 0 12px; font-size: 15px; font-weight: 600; line-height: 1.3; }
+.pop .options { padding: 0 0 12px; }
+.pop-actions { display: grid; grid-template-columns: 1fr 1fr; gap: 6px; }
+.pop-actions button { padding: 7px 0; border-radius: 9px; font-size: 13px; font-weight: 500; background: rgba(237,242,232,.07); }
+.pop-actions button:hover { background: rgba(237,242,232,.13); }
+.pop-actions button::before { content: ""; display: inline-block; width: 7px; height: 7px; border-radius: 50%; margin-right: 7px; background: var(--start); vertical-align: 1px; }
+.pop-actions .b-end::before { background: var(--end); }
+
+.dock { position: fixed; z-index: 2; right: max(16px, env(safe-area-inset-right)); bottom: max(16px, env(safe-area-inset-bottom)); display: flex; flex-direction: column; gap: 2px; padding: 3px; background: var(--panel); border: 1px solid var(--line); border-radius: 12px; backdrop-filter: blur(12px); -webkit-backdrop-filter: blur(12px); }
+.dock button { width: 32px; height: 32px; border-radius: 9px; color: var(--ink-2); display: grid; place-items: center; }
+.dock button:hover { background: var(--hover); color: var(--ink); }
+[hidden] { display: none !important; }
+.sr-only { position: absolute; width: 1px; height: 1px; padding: 0; margin: -1px; overflow: hidden; clip-path: inset(50%); white-space: nowrap; border: 0; }
+
+@media (max-width: 760px) {
+  .panel { left: 0; right: 0; top: auto; bottom: 0; width: auto; height: 56dvh; border-radius: 18px 18px 0 0; border-bottom: 0; padding-bottom: env(safe-area-inset-bottom); }
+  .panel-head { padding: 14px max(20px, env(safe-area-inset-left)) 2px; }
+  .ends, .results { padding-left: max(12px, env(safe-area-inset-left)); padding-right: max(12px, env(safe-area-inset-right)); }
+  .dock { flex-direction: row; bottom: calc(56dvh + 12px); }
+}
+@media (prefers-reduced-motion: reduce) { .skeleton { animation: none; } }
+
+.brand a { color: inherit; text-decoration: none; }
+.pop-details { display: block; width: 100%; margin-top: 6px; padding: 7px 0; color: var(--ink-2); font-size: 13px; }
+.pop-details:hover { color: var(--ink); }
+.size.pending { width: 34px; height: 21px; background: linear-gradient(90deg, rgba(237,242,232,.04), rgba(237,242,232,.12), rgba(237,242,232,.04)) 0 0 / 200% 100%; animation: shimmer 1.4s linear infinite; }
+.steps .rule-link { grid-column: 3; grid-row: 1; align-self: start; padding: 2px 0; background: none; color: var(--ink-3); font: 12px var(--mono); }
+.steps .rule-link:hover { color: var(--ink); text-decoration: underline; text-underline-offset: 3px; }
+#details-drawer { position: fixed; z-index: 5; top: calc(var(--header-height) + 16px); right: 16px; bottom: 16px; width: 440px; display: flex; flex-direction: column; background: var(--panel); border: 1px solid var(--line); border-radius: 18px; box-shadow: 0 24px 60px rgba(0,0,0,.45); backdrop-filter: blur(16px) saturate(1.1); -webkit-backdrop-filter: blur(16px) saturate(1.1); }
+.drawer-head { display: flex; justify-content: space-between; gap: 12px; padding: 18px 20px 14px; border-bottom: 1px solid var(--line); }
+.drawer-head > div { min-width: 0; }
+#details-title { margin: 0 0 6px; font-size: 15px; font-weight: 600; overflow-wrap: anywhere; }
+#drawer-atlas { font-size: 13px; color: var(--ink-2); text-decoration: none; }
+#drawer-atlas:hover { color: var(--ink); }
+#close-details { flex: none; width: 30px; height: 30px; border-radius: 50%; color: var(--ink-2); font-size: 22px; }
+#close-details:hover { color: var(--ink); background: var(--hover); }
+#drawer-body { flex: 1; min-height: 0; overflow: auto; padding: 4px 20px 20px; font-size: 16px; overflow-wrap: anywhere; overscroll-behavior: contain; }
+#drawer-body article { min-width: 0; }
+#drawer-body a { color: var(--accent); }
+@media (max-width: 1167px) {
+  #details-drawer { z-index: 10; inset: 0; width: auto; border: 0; border-radius: 0; padding: env(safe-area-inset-top) env(safe-area-inset-right) env(safe-area-inset-bottom) env(safe-area-inset-left); }
+}
+@media (prefers-reduced-motion: reduce) { .size.pending { animation: none; } }
diff --git a/docs/website/assets/site.css b/docs/website/src/styles/site.css
similarity index 92%
rename from docs/website/assets/site.css
rename to docs/website/src/styles/site.css
index 4292e033f..5622d1bd0 100644
--- a/docs/website/assets/site.css
+++ b/docs/website/src/styles/site.css
@@ -1,46 +1,39 @@
 @font-face {
   font-family: DM Sans;
-  src: url("./fonts/dm-sans-regular.ttf") format("truetype");
-  font-weight: 400;
-  font-style: normal;
-  font-display: swap;
-}
-@font-face {
-  font-family: DM Sans;
-  src: url("./fonts/dm-sans-semibold.ttf") format("truetype");
-  font-weight: 500 800;
+  src: url("../../assets/fonts/dm-sans-variable.woff2") format("woff2");
+  font-weight: 400 600;
   font-style: normal;
   font-display: swap;
 }
 @font-face {
   font-family: Instrument Serif;
-  src: url("./fonts/instrument-serif.ttf") format("truetype");
+  src: url("../../assets/fonts/instrument-serif.woff2") format("woff2");
   font-weight: 400;
   font-style: normal;
   font-display: swap;
 }
 @font-face {
   font-family: Instrument Serif;
-  src: url("./fonts/instrument-serif-italic.ttf") format("truetype");
+  src: url("../../assets/fonts/instrument-serif-italic.woff2") format("woff2");
   font-weight: 400;
   font-style: italic;
   font-display: swap;
 }
 :root {
   color-scheme: dark;
-  --surface: #162119;
-  --on-accent: #142016;
+  --surface: #121b15;
+  --on-accent: #13200f;
   --graph-node: #83a570;
   --diagram-selected: #c4dda6;
   --diagram-line: #88a079;
   --diagram-label: #c4d5b4;
-  --paper: #101713;
-  --ink: #e8ede5;
-  --muted: #a4b0a5;
-  --green: #c4dda6;
-  --line: #2c3b30;
-  --lime: #d5e9a7;
-  --pale: #1a271e;
+  --paper: #0b110d;
+  --ink: #eef3e9;
+  --muted: #a5b3a7;
+  --green: #cfe8a0;
+  --line: rgba(237, 242, 232, 0.1);
+  --lime: #cfe8a0;
+  --pale: #17221b;
   --serif: "Instrument Serif", Georgia, serif;
   --sans: "DM Sans", Arial, sans-serif;
   --mono: ui-monospace, SFMono-Regular, Consolas, monospace;
@@ -90,7 +83,8 @@ button:focus-visible,
 a:focus-visible,
 input:focus-visible,
 select:focus-visible,
-summary:focus-visible {
+summary:focus-visible,
+pre:focus-visible {
   outline: 3px solid var(--green);
   outline-offset: 5px;
 }
@@ -146,7 +140,7 @@ p {
   position: sticky;
   top: 0;
   z-index: 30;
-  background: rgba(16, 23, 19, 0.96);
+  background: rgba(11, 17, 13, 0.94);
   border-bottom: 1px solid var(--line);
   backdrop-filter: blur(16px);
 }
@@ -176,9 +170,6 @@ p {
 .site-footer .project-logo {
   width: 224px;
 }
-.brand-period {
-  color: var(--green);
-}
 .site-header nav {
   display: flex;
   flex-wrap: wrap;
@@ -198,8 +189,7 @@ p {
   text-decoration: underline;
   text-underline-offset: 9px;
 }
-.docs-nav span {
-  font-size: 13px;
+.docs-nav .arrow {
   margin-left: 3px;
 }
 .hero {
@@ -207,8 +197,8 @@ p {
   grid-template-columns: 1fr 1.15fr;
   gap: 40px;
   align-items: center;
-  min-height: 700px;
-  padding-block: 74px 76px;
+  min-height: 560px;
+  padding-block: 56px 48px;
 }
 .hero-copy {
   position: relative;
@@ -365,10 +355,11 @@ p {
   padding-left: 0;
 }
 .stats-bar > div strong {
-  font-size: 32px;
-  letter-spacing: -1.6px;
+  font-size: 34px;
+  letter-spacing: -1.4px;
   line-height: 1.25;
-  font-weight: 400;
+  font-weight: 500;
+  color: var(--lime);
 }
 .stats-bar > div span {
   font-size: 13px;
@@ -381,18 +372,18 @@ p {
   padding-left: 26px;
   border-left: 1px solid var(--line);
 }
-.stats-bar > a span {
-  margin-left: 16px;
+.stats-bar > a .arrow {
+  margin-left: 8px;
 }
 .section {
-  padding-block: 98px;
+  padding-block: 72px;
 }
 .section-heading {
   display: grid;
   grid-template-columns: 1.2fr 1fr;
   gap: 80px;
   align-items: end;
-  margin-bottom: 44px;
+  margin-bottom: 32px;
 }
 .section-heading > p,
 .section-heading > div > p {
@@ -467,18 +458,19 @@ p {
   font-size: 13px;
 }
 .research-section {
-  background: #1a3023;
+  border-top: 1px solid var(--line);
   color: var(--ink);
-  padding-block: 85px;
+  margin-top: 40px;
+  padding-block: 72px 64px;
 }
 .research-section p {
-  color: #b5c5b2;
+  color: var(--muted);
 }
 .research-cycle {
   display: grid;
   grid-template-columns: repeat(4, 1fr);
-  border-top: 1px solid #3a513d;
-  border-bottom: 1px solid #3a513d;
+  border-top: 1px solid var(--line);
+  border-bottom: 1px solid var(--line);
   margin-top: 55px;
 }
 .research-cycle article {
@@ -486,7 +478,7 @@ p {
 }
 .research-cycle article + article {
   padding-left: 25px;
-  border-left: 1px solid #3a513d;
+  border-left: 1px solid var(--line);
 }
 .research-cycle h3 {
   font-size: 18px;
@@ -564,7 +556,7 @@ p {
   width: 100%;
 }
 .infrastructure-section {
-  padding-block: 40px 104px;
+  padding-block: 72px 24px;
   display: grid;
   grid-template-columns: 1fr 1fr;
   gap: 70px;
@@ -838,6 +830,8 @@ pre {
 }
 .atlas-row {
   display: grid;
+  content-visibility: auto;
+  contain-intrinsic-size: auto 160px;
   grid-template-columns: 1fr auto;
   gap: 24px;
   padding: 18px 0;
@@ -1004,20 +998,6 @@ pre {
   color: var(--ink);
   font-size: 15px;
 }
-.variant-tags {
-  display: flex;
-  flex-wrap: wrap;
-  gap: 6px;
-  margin-top: 18px;
-}
-.variant-tag {
-  border: 1px solid var(--line);
-  border-radius: 3px;
-  padding: 4px 8px;
-  font-family: var(--mono);
-  font-size: 13px;
-  color: var(--muted);
-}
 .relation-link {
   display: flex;
   align-items: center;
@@ -1216,12 +1196,6 @@ pre {
   .hero h1 {
     font-size: 74px;
   }
-  .hero h1 br.desktop-break {
-    display: none;
-  }
-.hero-description {
-    font-size: 16px;
-  }
   .hero-copy {
     max-width: 600px;
   }
@@ -1307,7 +1281,7 @@ pre {
     border-left: 0;
   }
   .research-cycle article:nth-child(n + 3) {
-    border-top: 1px solid #3a513d;
+    border-top: 1px solid var(--line);
   }
   .research-note {
     flex-wrap: wrap;
@@ -1339,7 +1313,6 @@ pre {
   }
   .infrastructure-section {
     grid-template-columns: 1fr;
-    gap: 35px;
     padding-block: 15px 65px;
   }
   .terminal {
@@ -1441,20 +1414,15 @@ pre {
   }
 .site-header nav {
     gap: 13px;
-    font-size: 14px;
   }
   .hero h1 {
     font-size: 61px;
   }
-.hero-description {
-    font-size: 16px;
-  }
   .hero-actions {
     gap: 20px;
   }
 .button {
     padding: 11px 16px;
-    font-size: 14px;
   }
 .hero-actions .text-link {
     font-size: 14px;
@@ -1475,18 +1443,12 @@ pre {
   .problem-card h3 {
     font-size: 21px;
   }
-.problem-card p {
-    font-size: 15px;
-  }
   .research-cycle article {
     padding: 22px 16px !important;
   }
   .research-cycle h3 {
     font-size: 16px;
   }
-.research-cycle p {
-    font-size: 15px;
-  }
   .section-bottom {
     flex-direction: column;
     gap: 10px;
@@ -1509,3 +1471,26 @@ pre {
     transition: none !important;
   }
 }
+
+.arrow {
+  display: inline-block;
+  width: 0.95em;
+  height: 0.95em;
+  flex: none;
+  vertical-align: -0.12em;
+  background: currentColor;
+  -webkit-mask: var(--arrow) center / contain no-repeat;
+  mask: var(--arrow) center / contain no-repeat;
+  --arrow: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='none' stroke='black' stroke-width='1.8' stroke-linecap='round' stroke-linejoin='round'%3E%3Cpath d='M3 8h9M8.5 4.5 12 8l-3.5 3.5'/%3E%3C/svg%3E");
+}
+.arrow.ne {
+  --arrow: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='none' stroke='black' stroke-width='1.8' stroke-linecap='round' stroke-linejoin='round'%3E%3Cpath d='M5 11 11 5M6 5h5v5'/%3E%3C/svg%3E");
+}
+.arrow.w {
+  --arrow: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='none' stroke='black' stroke-width='1.8' stroke-linecap='round' stroke-linejoin='round'%3E%3Cpath d='M13 8H4M7.5 4.5 4 8l3.5 3.5'/%3E%3C/svg%3E");
+}
+.atlas-row > .arrow {
+  align-self: center;
+  width: 20px;
+  height: 20px;
+}
diff --git a/docs/website/src/workers/path-selection.d.ts b/docs/website/src/workers/path-selection.d.ts
new file mode 100644
index 000000000..a4a66e451
--- /dev/null
+++ b/docs/website/src/workers/path-selection.d.ts
@@ -0,0 +1,47 @@
+/* tslint:disable */
+/* eslint-disable */
+
+/**
+ * Compare exactly the routes returned by `find_paths`, retaining their one-based indices.
+ */
+
+export function find_paths(input: string): string;
+
+/**
+ * Browser result: certificates, all pair counts and the front, without pair records.
+ */
+export function summarize_paths(input: string): string;
+
+export type InitInput = RequestInfo | URL | Response | BufferSource | WebAssembly.Module;
+
+export interface InitOutput {
+    readonly memory: WebAssembly.Memory;
+    readonly find_paths: (a: number, b: number, c: number) => void;
+    readonly summarize_paths: (a: number, b: number, c: number) => void;
+    readonly __wbindgen_add_to_stack_pointer: (a: number) => number;
+    readonly __wbindgen_export: (a: number, b: number) => number;
+    readonly __wbindgen_export2: (a: number, b: number, c: number, d: number) => number;
+    readonly __wbindgen_export3: (a: number, b: number, c: number) => void;
+}
+
+export type SyncInitInput = BufferSource | WebAssembly.Module;
+
+/**
+ * Instantiates the given `module`, which can either be bytes or
+ * a precompiled `WebAssembly.Module`.
+ *
+ * @param {{ module: SyncInitInput }} module - Passing `SyncInitInput` directly is deprecated.
+ *
+ * @returns {InitOutput}
+ */
+export function initSync(module: { module: SyncInitInput } | SyncInitInput): InitOutput;
+
+/**
+ * If `module_or_path` is {RequestInfo} or {URL}, makes a request and
+ * for everything else, calls `WebAssembly.instantiate` directly.
+ *
+ * @param {{ module_or_path: InitInput | Promise<InitInput> }} module_or_path - Passing `InitInput` directly is deprecated.
+ *
+ * @returns {Promise<InitOutput>}
+ */
+export default function __wbg_init (module_or_path?: { module_or_path: InitInput | Promise<InitInput> } | InitInput | Promise<InitInput>): Promise<InitOutput>;
diff --git a/docs/website/src/workers/path-worker.ts b/docs/website/src/workers/path-worker.ts
new file mode 100644
index 000000000..7802c4342
--- /dev/null
+++ b/docs/website/src/workers/path-worker.ts
@@ -0,0 +1,60 @@
+import type { Query } from '../generated/wasm-path-request.mjs';
+import type { ComparisonQuery } from '../generated/wasm-comparison-request.mjs';
+import init, { find_paths, summarize_paths } from "./path-selection.js";
+import type { WasmPathResult } from '../generated/wasm-paths.mjs';
+import type { WasmComparisonResult } from '../generated/wasm-comparison.mjs';
+import type { PathGraphData } from '../generated/path-graph.mjs';
+import { validatePathRequest, type PathRequest, type PathReply } from '../lib/path-worker-data.mts';
+
+performance.mark("engine:script");
+const graph = fetch(new URL('./path-graph.json.gz', import.meta.url)).then(async (response) => {
+  if (!response.ok) throw new Error(`Cannot load path metadata (${response.status})`);
+  const text = await new Response(response.body!.pipeThrough(new DecompressionStream('gzip'))).text();
+  performance.mark("engine:metadata-decoded");
+  const result = JSON.parse(text) as PathGraphData;
+  performance.mark("engine:metadata-parsed");
+  return result;
+});
+let engine: Promise<void> | undefined;
+function loadEngine() {
+  return engine ||= (async () => {
+    performance.mark("engine:fetch");
+    const response = await fetch(new URL('./path-selection_bg.wasm.gz', import.meta.url));
+    performance.mark("engine:headers");
+    if (!response.ok) throw new Error(`Cannot load path engine (${response.status})`);
+    const wasm = response.body!.pipeThrough(new DecompressionStream('gzip'));
+    // shortcut: Buffering avoids a Firefox streaming stall; revisit if module growth makes this buffer material.
+    const bytes = await new Response(wasm).arrayBuffer();
+    performance.mark("engine:wasm-decoded");
+    await init({module_or_path: bytes});
+    performance.mark("engine:initialized");
+  })();
+}
+const ready = Promise.all([loadEngine(), graph]);
+ready.catch(() => {});
+
+self.onmessage = async ({data}: MessageEvent<PathRequest>) => {
+  performance.mark("engine:request-received");
+  let phase: PathReply['phase'] = "paths";
+  try {
+    const [, graph] = await ready;
+    const started = performance.now();
+    const request = validatePathRequest(data);
+    performance.measure('engine:request-validation', {start: started});
+    performance.mark("engine:paths-start");
+    const result: WasmPathResult = request.kind === 'compare' ? request.cached : JSON.parse(find_paths(JSON.stringify({
+      graph, source: request.source, target: request.target, limit: request.limit,
+    } satisfies Query)));
+    performance.mark("engine:paths-end");
+    if (request.kind === 'search') self.postMessage({phase: 'paths', result} satisfies PathReply);
+    phase = "comparison";
+    if (result.paths.length) {
+      performance.mark("engine:comparison-start");
+      const comparison: WasmComparisonResult = JSON.parse(summarize_paths(JSON.stringify({graph, paths: result.paths} satisfies ComparisonQuery)));
+      performance.mark("engine:comparison-end");
+      self.postMessage({phase: 'comparison', result: comparison} satisfies PathReply);
+    }
+  } catch (error) {
+    self.postMessage({phase, error: error instanceof Error ? error.message : String(error)} satisfies PathReply);
+  }
+};
diff --git a/eslint.config.mjs b/eslint.config.mjs
new file mode 100644
index 000000000..0cd911e03
--- /dev/null
+++ b/eslint.config.mjs
@@ -0,0 +1,22 @@
+import tsParser from '@typescript-eslint/parser';
+
+export default [{ ignores: ['docs/website/src/workers/path-selection.d.ts'] }, {
+  files: ['docs/website/src/**/*.{js,mjs,ts,mts}', 'scripts/{build_frontend,generate_website_contracts,validate_website_data,website_contracts}.mjs'],
+  rules: {
+    'constructor-super': 'error',
+    'for-direction': 'error',
+    'no-constant-condition': 'error',
+    'no-dupe-args': 'error',
+    'no-dupe-class-members': 'error',
+    'no-dupe-else-if': 'error',
+    'no-duplicate-case': 'error',
+    'no-duplicate-imports': 'error',
+    'no-unreachable': 'error',
+    'no-unsafe-finally': 'error',
+    'use-isnan': 'error',
+    'valid-typeof': 'error',
+  },
+}, {
+  files: ['docs/website/src/**/*.{ts,mts}'],
+  languageOptions: { parser: tsParser },
+}];
diff --git a/examples/polynomial_compare_audit.rs b/examples/polynomial_compare_audit.rs
new file mode 100644
index 000000000..5a4c77e71
--- /dev/null
+++ b/examples/polynomial_compare_audit.rs
@@ -0,0 +1,120 @@
+//! Verdict distribution of the V1 polynomial comparator over every simple path of
+//! 1-4 non-Turing hops in the registered reduction graph, grouped by variant endpoints.
+//! Simple means no repeated (problem name, complete variant) node; variant casts count
+//! as hops. Uncomposable paths are counted as skipped and excluded from comparisons.
+//! Each endpoint group is one generic batch, including every nonzero field certificate.
+//!
+//! cargo run --release --example polynomial_compare_audit
+use problemreductions::poly_compare::{compare_all, Direction, Profile, Reason, Verdict};
+use problemreductions::rules::{ReductionGraph, ReductionPath, ReductionStep};
+use std::collections::BTreeMap;
+use std::time::Instant;
+
+const MAX_HOPS: usize = 4;
+
+type Node = (String, BTreeMap<String, String>);
+
+fn extend(graph: &ReductionGraph, path: &mut Vec<Node>, found: &mut Vec<ReductionPath>) {
+    if path.len() > MAX_HOPS {
+        return;
+    }
+    let (name, variant) = path.last().expect("non-empty path").clone();
+    for edge in graph.outgoing_reductions(&name) {
+        if edge.source_variant != variant || edge.capabilities.turing {
+            continue;
+        }
+        let next = (edge.target_name.to_string(), edge.target_variant);
+        if path.contains(&next) {
+            continue;
+        }
+        path.push(next);
+        found.push(ReductionPath {
+            steps: path
+                .iter()
+                .map(|(name, variant)| ReductionStep {
+                    name: name.clone(),
+                    variant: variant.clone(),
+                })
+                .collect(),
+        });
+        extend(graph, path, found);
+        path.pop();
+    }
+}
+
+fn record_reason(field: &str, reason: &Reason, totals: &mut BTreeMap<String, usize>) {
+    let kind = match reason {
+        Reason::NotPolynomial(_) => "not polynomial",
+        Reason::Unavailable(_) => "unavailable",
+        Reason::MissingField => "missing field",
+        Reason::Validity => "validity",
+        Reason::ResourceLimit(_) => "resource limit",
+    };
+    *totals.entry(format!("{kind} ({field})")).or_default() += 1;
+}
+
+fn main() {
+    let graph = ReductionGraph::new();
+    let started = Instant::now();
+    let mut paths = Vec::new();
+    for name in graph.problem_types() {
+        for variant in graph.variants_for(name) {
+            extend(&graph, &mut vec![(name.to_string(), variant)], &mut paths);
+        }
+    }
+    let mut groups: BTreeMap<(String, String), Vec<Profile>> = BTreeMap::new();
+    let mut skipped = 0;
+    for path in &paths {
+        let (Some(first), Some(last)) = (path.steps.first(), path.steps.last()) else {
+            continue;
+        };
+        match graph.path_polynomial_profile(path) {
+            Ok(profile) => groups
+                .entry((first.to_string(), last.to_string()))
+                .or_default()
+                .push(profile),
+            Err(_) => skipped += 1,
+        }
+    }
+    let enumerated = started.elapsed();
+    let mut counts = [0; 4];
+    let mut front = 0;
+    let mut reasons = BTreeMap::new();
+    for profiles in groups.values() {
+        let result = compare_all(profiles);
+        for (_, _, pair) in &result.pairs {
+            for (field, f) in &pair.fields {
+                if pair.verdict == Verdict::Unknown {
+                    for direction in [&f.forward, &f.reverse] {
+                        if let Direction::Unknown(reason) = direction {
+                            record_reason(field, reason, &mut reasons);
+                        }
+                    }
+                }
+            }
+        }
+        for (total, count) in counts.iter_mut().zip(result.counts()) {
+            *total += count;
+        }
+        front += result.front.len();
+    }
+    println!(
+        "paths: {} ({skipped} without a composable transform)",
+        paths.len()
+    );
+    println!("endpoint pairs: {}", groups.len());
+    println!("generic comparison (batch-relative; regular valid families):");
+    for (name, count) in Verdict::ALL.iter().zip(counts) {
+        println!("{name}: {count}");
+    }
+    println!("unresolved directions in Unknown pairs, by reason (field):");
+    for (reason, count) in &reasons {
+        println!("  {reason}: {count}");
+    }
+    println!("candidate front size (summed over endpoint pairs): {front}");
+    println!(
+        "time: {:.2?} enumeration and composition, {:.2?} total",
+        enumerated,
+        started.elapsed()
+    );
+}
diff --git a/package-lock.json b/package-lock.json
index b741a0525..83a1adc9c 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -6,57 +6,2234 @@
     "": {
       "name": "problemreductions-docs",
       "devDependencies": {
+        "@typescript-eslint/parser": "8.71.2",
+        "ajv": "8.20.0",
+        "axe-core": "4.14.0",
         "cytoscape": "3.33.1",
         "cytoscape-fcose": "2.2.0",
-        "elkjs": "0.9.3"
+        "elkjs": "0.9.3",
+        "eslint": "10.12.0",
+        "json-schema-to-typescript": "16.0.0",
+        "typescript": "6.0.3",
+        "vite": "8.3.4"
       }
     },
-    "node_modules/cose-base": {
+    "node_modules/@apidevtools/json-schema-ref-parser": {
+      "version": "11.9.3",
+      "resolved": "https://registry.npmjs.org/@apidevtools/json-schema-ref-parser/-/json-schema-ref-parser-11.9.3.tgz",
+      "integrity": "sha512-60vepv88RwcJtSHrD6MjIL6Ta3SOYbgfnkHb+ppAVK+o9mXprRtulx7VlRl3lN3bbvysAfCS7WMVfhUYemB0IQ==",
+      "dev": true,
+      "license": "MIT",
+      "dependencies": {
+        "@jsdevtools/ono": "^7.1.3",
+        "@types/json-schema": "^7.0.15",
+        "js-yaml": "^4.1.0"
+      },
+      "engines": {
+        "node": ">= 16"
+      },
+      "funding": {
+        "url": "https://github.com/sponsors/philsturgeon"
+      }
+    },
+    "node_modules/@apidevtools/json-schema-ref-parser/node_modules/argparse": {
+      "version": "2.0.1",
+      "resolved": "https://registry.npmjs.org/argparse/-/argparse-2.0.1.tgz",
+      "integrity": "sha512-8+9WqebbFzpX9OR+Wa6O29asIogeRMzcGtAINdpMHHyAg10f05aSFVBbcEqGf/PXw1EjAZ+q2/bEBg3DvurK3Q==",
+      "dev": true,
+      "license": "Python-2.0"
+    },
+    "node_modules/@apidevtools/json-schema-ref-parser/node_modules/js-yaml": {
+      "version": "4.3.2",
+      "resolved": "https://registry.npmjs.org/js-yaml/-/js-yaml-4.3.2.tgz",
+      "integrity": "sha512-SFNOvSJ+Dgf/9An904Yx+CgSlIPCkIpao4qo51lpee25TIRejdH3rhR4EZMGoNx3/TP3O+wzWuiTFl4sqbltzA==",
+      "dev": true,
+      "funding": [
+        {
+          "type": "github",
+          "url": "https://github.com/sponsors/puzrin"
+        },
+        {
+          "type": "github",
+          "url": "https://github.com/sponsors/nodeca"
+        }
+      ],
+      "license": "MIT",
+      "dependencies": {
+        "argparse": "^2.0.1"
+      },
+      "bin": {
+        "js-yaml": "bin/js-yaml.js"
+      }
+    },
+    "node_modules/@cacheable/memory": {
       "version": "2.2.0",
-      "resolved": "https://registry.npmjs.org/cose-base/-/cose-base-2.2.0.tgz",
-      "integrity": "sha512-AzlgcsCbUMymkADOJtQm3wO9S3ltPfYOFD5033keQn9NJzIbtnZj+UdBJe7DYml/8TdbtHJW3j58SOnKhWY/5g==",
+      "resolved": "https://registry.npmjs.org/@cacheable/memory/-/memory-2.2.0.tgz",
+      "integrity": "sha512-CTLKqLItRCEixEAewD3/j9DB3/o96gpTPD4eJ1v+DGOlxZRZncRQkGYqqnAGCscYd6RNeXfGeiuCphsPtqyIfQ==",
       "dev": true,
       "license": "MIT",
       "dependencies": {
-        "layout-base": "^2.0.0"
+        "@cacheable/utils": "^2.5.0",
+        "@keyv/bigmap": "^1.3.1",
+        "hookified": "^1.15.1",
+        "keyv": "^5.6.0"
       }
     },
-    "node_modules/cytoscape": {
-      "version": "3.33.1",
-      "resolved": "https://registry.npmjs.org/cytoscape/-/cytoscape-3.33.1.tgz",
-      "integrity": "sha512-iJc4TwyANnOGR1OmWhsS9ayRS3s+XQ185FmuHObThD+5AeJCakAAbWv8KimMTt08xCCLNgneQwFp+JRJOr9qGQ==",
+    "node_modules/@cacheable/utils": {
+      "version": "2.5.0",
+      "resolved": "https://registry.npmjs.org/@cacheable/utils/-/utils-2.5.0.tgz",
+      "integrity": "sha512-buipgOVDkkPXNR5+xBpDw7Zk2n1EvU7qBJCNUcL7rhQ//kfpOXPAvQ511Os0vpLYJ1pZnvudNytkQt2hst3wqA==",
+      "dev": true,
+      "license": "MIT",
+      "dependencies": {
+        "hashery": "^1.5.1",
+        "keyv": "^5.6.0"
+      }
+    },
+    "node_modules/@eslint-community/eslint-utils": {
+      "version": "4.10.1",
+      "resolved": "https://registry.npmjs.org/@eslint-community/eslint-utils/-/eslint-utils-4.10.1.tgz",
+      "integrity": "sha512-cuadcxVFE8sDK6iWJbs8Sn0av2Nrh2QSGQhVlBW9AaAHqHwjWsZHT8LJ4hFGPh7ASBV2deFdM7H/DPjulmh8rg==",
       "dev": true,
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+      }
+    },
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+        "stylus": ">=0.54.8",
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+      "dev": true,
+      "license": "ISC",
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+      },
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+        "node-which": "bin/node-which"
+      },
+      "engines": {
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+      }
+    },
+    "node_modules/word-wrap": {
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+      "dev": true,
+      "license": "MIT",
+      "engines": {
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+    "node_modules/yocto-queue": {
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+      "resolved": "https://registry.npmjs.org/yocto-queue/-/yocto-queue-0.1.0.tgz",
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+      "dev": true,
+      "license": "MIT",
+      "engines": {
+        "node": ">=10"
+      },
+      "funding": {
+        "url": "https://github.com/sponsors/sindresorhus"
+      }
     }
   }
 }
diff --git a/package.json b/package.json
index 3cf29e7da..277f84d5b 100644
--- a/package.json
+++ b/package.json
@@ -2,12 +2,26 @@
   "name": "problemreductions-docs",
   "private": true,
   "scripts": {
+    "build:frontend": "node scripts/build_frontend.mjs",
+    "typecheck": "tsc --project tsconfig.json",
+    "lint:frontend": "eslint docs/website/src scripts/build_frontend.mjs scripts/generate_website_contracts.mjs scripts/validate_website_data.mjs scripts/test_website_contracts.mjs scripts/test_website_growth.mjs scripts/website_contracts.mjs",
     "generate:reduction-graph-layout": "node scripts/generate_reduction_graph_layout.js",
-    "test:reduction-graph-js": "node scripts/test_reduction_graph_js.js && node scripts/test_reduction_graph_layout_generator.js"
+    "test:reduction-graph-js": "node scripts/test_reduction_graph_js.js && node scripts/test_reduction_graph_layout_generator.js",
+    "generate:frontend-contracts": "cargo run --locked -p problemreductions-web --features schema-export --example export_frontend_schema | node scripts/generate_website_contracts.mjs",
+    "test:frontend-contracts": "node --test scripts/test_website_contracts.mjs scripts/test_website_growth.mjs",
+    "pretypecheck": "npm run generate:frontend-contracts",
+    "pretest:frontend-contracts": "npm run generate:frontend-contracts"
   },
   "devDependencies": {
+    "@typescript-eslint/parser": "8.71.2",
+    "ajv": "8.20.0",
+    "axe-core": "4.14.0",
     "cytoscape": "3.33.1",
     "cytoscape-fcose": "2.2.0",
-    "elkjs": "0.9.3"
+    "elkjs": "0.9.3",
+    "eslint": "10.12.0",
+    "json-schema-to-typescript": "16.0.0",
+    "typescript": "6.0.3",
+    "vite": "8.3.4"
   }
 }
diff --git a/problemreductions-cli/src/cli.rs b/problemreductions-cli/src/cli.rs
index b841d6a1f..05edafeb9 100644
--- a/problemreductions-cli/src/cli.rs
+++ b/problemreductions-cli/src/cli.rs
@@ -185,6 +185,12 @@ Use `pred list` to see available problems.")]
         limit: usize,
         /// Source problem instance JSON. When present, execute every returned path and measure each constructed problem.
         instance: Option<std::path::PathBuf>,
+        /// Compare chosen polynomial certificates in the batch-relative generic order.
+        #[arg(long, conflicts_with = "instance")]
+        compare: bool,
+        /// Show detailed pair verdicts, per-field proofs, and counterexample curves.
+        #[arg(long, requires = "compare")]
+        proofs: bool,
     },
 
     /// Export the reduction graph to JSON
diff --git a/problemreductions-cli/src/commands/graph.rs b/problemreductions-cli/src/commands/graph.rs
index 53d94812c..8f489745e 100644
--- a/problemreductions-cli/src/commands/graph.rs
+++ b/problemreductions-cli/src/commands/graph.rs
@@ -11,6 +11,9 @@ use std::any::Any;
 use std::collections::BTreeMap;
 use std::path::Path;
 
+#[path = "graph_compare.rs"]
+mod compare_view;
+
 pub fn list(
     query: Option<&str>,
     category: Option<ProblemCategory>,
@@ -776,24 +779,25 @@ fn prepare_overall_parameters(
         .collect()
 }
 
+/// Path header showing every problem variant.
+fn fmt_path_chain(graph: &ReductionGraph, reduction_path: &ReductionPath) -> String {
+    reduction_path
+        .steps
+        .iter()
+        .map(|step| fmt_node(graph, &step.name, &step.variant))
+        .collect::<Vec<_>>()
+        .join(&format!(" {} ", crate::output::fmt_outgoing("→")))
+}
+
 fn format_path_text(
     graph: &ReductionGraph,
     reduction_path: &problemreductions::rules::ReductionPath,
 ) -> String {
-    // Build formatted path header: Name {v} → Name {v} → ...
-    let path_summary = {
-        let steps = &reduction_path.steps;
-        let mut parts = Vec::new();
-        let mut prev_name = "";
-        for step in steps {
-            if step.name != prev_name {
-                parts.push(fmt_node(graph, &step.name, &step.variant));
-                prev_name = &step.name;
-            }
-        }
-        parts.join(&format!(" {} ", crate::output::fmt_outgoing("→")))
-    };
-    let mut text = format!("Path ({} steps): {}\n", reduction_path.len(), path_summary);
+    let mut text = format!(
+        "Path ({} steps): {}\n",
+        reduction_path.len(),
+        fmt_path_chain(graph, reduction_path)
+    );
 
     let steps = &reduction_path.steps;
     for i in 0..steps.len().saturating_sub(1) {
@@ -897,6 +901,8 @@ pub fn path(
     target: &str,
     limit: usize,
     instance: Option<&Path>,
+    compare: bool,
+    proofs: bool,
     out: &OutputConfig,
 ) -> Result<()> {
     let src_spec = parse_problem_spec(source)?;
@@ -960,6 +966,8 @@ pub fn path(
             &dst_ref.name,
             &dst_ref.variant,
             limit,
+            compare,
+            proofs,
             out,
         )
     }
@@ -973,6 +981,8 @@ fn path_symbolic(
     dst_name: &str,
     dst_variant: &BTreeMap<String, String>,
     limit: usize,
+    compare: bool,
+    proofs: bool,
     out: &OutputConfig,
 ) -> Result<()> {
     let batch = find_path_batch(graph, src_name, src_variant, dst_name, dst_variant, limit)?;
@@ -991,18 +1001,43 @@ fn path_symbolic(
             dst_name,
         );
     }
+    let comparison = if compare {
+        let profiles = batch
+            .paths
+            .iter()
+            .map(|p| graph.path_polynomial_profile(p))
+            .collect::<std::result::Result<Vec<_>, _>>()?;
+        Some(compare_view::ComparisonView::new(profiles))
+    } else {
+        None
+    };
     out.emit(
         || {
-            render_paths_text(
-                graph,
-                &batch.paths,
-                src_name,
-                dst_name,
-                batch.truncated,
-                limit,
-            )
+            if let Some(view) = &comparison {
+                let mut text = view.render(graph, &batch.paths, proofs);
+                if batch.truncated {
+                    text.push_str(path_truncation_note(limit));
+                    text.push('\n');
+                }
+                text
+            } else {
+                render_paths_text(
+                    graph,
+                    &batch.paths,
+                    src_name,
+                    dst_name,
+                    batch.truncated,
+                    limit,
+                )
+            }
+        },
+        || {
+            let mut value = path_batch_json(graph, &batch, None)?;
+            if let Some(view) = &comparison {
+                value["polynomial_comparison"] = view.to_json();
+            }
+            Ok(value)
         },
-        || path_batch_json(graph, &batch, None),
     )
 }
 
@@ -1322,7 +1357,63 @@ fn render_tree(graph: &ReductionGraph, nodes: &[NeighborTree], text: &mut String
 
 #[cfg(test)]
 mod tests {
-    use super::push_alias_part;
+    use super::{compare_view::ComparisonView, push_alias_part};
+
+    #[test]
+    fn polynomial_view_distinguishes_incomparable_from_unknown_and_keeps_candidates() {
+        use problemreductions::{expr::Expr, parameters::ParameterRelation, poly_compare::*};
+        let profile = |s| {
+            Profile::new(std::collections::BTreeMap::from([(
+                "size".into(),
+                FieldCertificate::new(&Expr::parse(s), ParameterRelation::Exact),
+            )]))
+        };
+        let view =
+            ComparisonView::new(vec![profile("n"), profile("m"), profile("n^2-m")]).to_json();
+        assert_eq!(view["pairs"][0]["verdict"], "Incomparable");
+        assert_eq!(view["pairs"][1]["verdict"], "Dominated");
+        assert_eq!(view["front"], serde_json::json!([1, 2]));
+        assert_eq!(
+            view["pairs"][0]["fields"]["size"]["forward"]["status"],
+            "No"
+        );
+        assert_eq!(view["schema_version"], 5);
+        assert!(view["pairs"][0]["fields"]["size"]["forward"]["certificate"]["curve"].is_object());
+        assert_eq!(
+            view["pairs"][1]["fields"]["size"]["forward"]["status"],
+            "Yes"
+        );
+        let unresolved =
+            ComparisonView::new(vec![profile("m"), profile("n"), profile("n-m")]).to_json();
+        assert_eq!(unresolved["pairs"][0]["verdict"], "Unknown");
+        assert_eq!(
+            unresolved["pairs"][0]["fields"]["size"]["forward"]["missing_obligation"]["kind"],
+            "validity"
+        );
+        let view = ComparisonView::new(vec![profile("n^2+m^2-n*m"), profile("n^2+m^2")]).to_json();
+        let field = &view["pairs"][0]["fields"]["size"];
+        assert_eq!(field["forward"]["status"], "Yes");
+        assert_eq!(field["forward"]["certificate"]["kind"], "newton");
+        assert_eq!(
+            field["forward"]["certificate"].as_object().unwrap().len(),
+            2
+        );
+        assert_eq!(field["reverse"]["status"], "Yes");
+        assert_eq!(view["front"], serde_json::json!([1, 2]));
+        assert_eq!(view["pairs"][0]["verdict"], "Equivalent");
+        for (formulas, winner, loser) in [(["n", "n^2"], 1, 2), (["n^2", "n"], 2, 1)] {
+            let view = ComparisonView::new(formulas.into_iter().map(profile).collect()).to_json();
+            assert_eq!(
+                view["pairs"][0]["dominates"],
+                serde_json::json!({"winner":winner,"loser":loser})
+            );
+            assert_eq!(view["front"], serde_json::json!([winner]));
+            assert_eq!(
+                view["pairs"][0]["description"],
+                format!("Path {winner} dominates Path {loser} (strict on: size)")
+            );
+        }
+    }
 
     #[test]
     fn push_alias_part_deduplicates_case_insensitively_in_order() {
diff --git a/problemreductions-cli/src/commands/graph_compare.rs b/problemreductions-cli/src/commands/graph_compare.rs
new file mode 100644
index 000000000..a195e9d2b
--- /dev/null
+++ b/problemreductions-cli/src/commands/graph_compare.rs
@@ -0,0 +1,277 @@
+//! Presentation only: decisions and the front come from `poly_compare::compare_all`.
+use super::{fmt_path_chain, ReductionGraph, ReductionPath};
+use problemreductions::poly_compare::{
+    compare_all, Direction, PathComparison, Profile, ProfileComparison, Side, Verdict,
+};
+use serde_json::{json, Value};
+
+/// 1-based `(winner, loser)` of a dominated pair.
+fn winner_loser(i: usize, j: usize, verdict: Verdict) -> Option<(usize, usize)> {
+    verdict.winner_loser(i, j).map(|(w, l)| (w + 1, l + 1))
+}
+
+fn strict_fields(c: &ProfileComparison, worse: Side) -> String {
+    c.fields
+        .iter()
+        .filter(|(_, f)| f.verdict() == Verdict::Dominated { worse })
+        .map(|(n, _)| n.as_str())
+        .collect::<Vec<_>>()
+        .join(", ")
+}
+
+fn description(i: usize, j: usize, c: &ProfileComparison) -> String {
+    let (a, b) = (i + 1, j + 1);
+    let verdict = c.verdict;
+    match verdict {
+        Verdict::Dominated { worse } => {
+            let (winner, loser) = winner_loser(i, j, verdict).expect("dominated");
+            format!(
+                "Path {winner} dominates Path {loser} (strict on: {})",
+                strict_fields(c, worse)
+            )
+        }
+        Verdict::Equivalent => format!("Path {a} ≡ Path {b}"),
+        Verdict::Unknown => "UNRESOLVED (details below)".into(),
+        Verdict::Incomparable => {
+            let mut details = Vec::new();
+            for (path, worse) in [(a, Side::Right), (b, Side::Left)] {
+                let fields = strict_fields(c, worse);
+                if !fields.is_empty() {
+                    details.push(format!("Path {path} better on {fields}"));
+                }
+            }
+            for (name, f) in &c.fields {
+                match f.verdict() {
+                    Verdict::Incomparable => {
+                        details.push(format!("{name}: mutually unbounded ratios"))
+                    }
+                    Verdict::Unknown => {
+                        for (no, left, right) in [
+                            (matches!(f.forward, Direction::No(_)), a, b),
+                            (matches!(f.reverse, Direction::No(_)), b, a),
+                        ] {
+                            if no {
+                                details.push(format!("{name}: Path {left} is not O(Path {right})"));
+                            }
+                        }
+                    }
+                    _ => {}
+                }
+            }
+            format!("proven incomparable — {}", details.join("; "))
+        }
+    }
+}
+
+pub(super) struct ComparisonView {
+    profiles: Vec<Profile>,
+    result: PathComparison,
+}
+impl ComparisonView {
+    pub(super) fn new(profiles: Vec<Profile>) -> Self {
+        let result = compare_all(&profiles);
+        Self { profiles, result }
+    }
+
+    pub(super) fn to_json(&self) -> Value {
+        let counts = self.result.counts();
+        json!({
+            "schema_version": 5,
+            "mode": "generic",
+            "domain": "growth families x_i = c_i*t^e_i; c_i >= 2, e_i >= 0, e != 0",
+            "counts": Verdict::ALL.iter().zip(counts).collect::<std::collections::BTreeMap<_, _>>(),
+            "scope": "all nonzero polynomial certificates in profiles; regular and positive top faces",
+            "front": self.result.front.iter().map(|i| i + 1).collect::<Vec<_>>(),
+            "pairs": self.result.pairs.iter().map(|(i, j, c)| {
+                let mut pair = json!({
+                    "paths": [i + 1, j + 1],
+                    "verdict": c.verdict,
+                    "description": description(*i, *j, c),
+                    "fields": c.fields,
+                });
+                if let Some((winner, loser)) = winner_loser(*i, *j, c.verdict) {
+                    pair["dominates"] = json!({"winner": winner, "loser": loser});
+                }
+                pair
+            }).collect::<Vec<_>>(),
+            "profiles": self.profiles,
+        })
+    }
+
+    pub(super) fn render(
+        &self,
+        graph: &ReductionGraph,
+        paths: &[ReductionPath],
+        proofs: bool,
+    ) -> String {
+        let mut text = String::from("Polynomial comparison: generic order of chosen certificates, batch-relative regular valid growth families; smaller certificates are better. Ignores exact-cancellation families such as complete graphs; keeps bounded strata and exponent cells.\n");
+        text.push_str(&format!(
+            "\nPair verdicts ({} pairs):\n",
+            self.result.pairs.len()
+        ));
+        let [dominated, equivalent, incomparable, unknown] = self.result.counts();
+        text.push_str(&format!("  {dominated} dominated, {equivalent} equivalent, {incomparable} proven incomparable, {unknown} unresolved\n"));
+        for (i, j, c) in &self.result.pairs {
+            text.push_str(&format!(
+                "  Paths {}, {}: {}\n",
+                i + 1,
+                j + 1,
+                description(*i, *j, c)
+            ));
+        }
+        text.push_str("\nUnresolved pairs:\n");
+        if self.result.counts()[3] == 0 {
+            text.push_str("  None.\n");
+        }
+        for (i, j, c) in self
+            .result
+            .pairs
+            .iter()
+            .filter(|(_, _, c)| c.verdict == Verdict::Unknown)
+        {
+            text.push_str(&format!("  Paths {}, {}:\n", i + 1, j + 1));
+            for (name, f) in &c.fields {
+                for (d, left, right) in [(&f.forward, i + 1, j + 1), (&f.reverse, j + 1, i + 1)] {
+                    if let Direction::Unknown(reason) = d {
+                        text.push_str(&format!(
+                            "    {name}, Path {left} ≤O Path {right}: missing obligation: {reason}\n"
+                        ));
+                    }
+                }
+            }
+        }
+        text.push_str("\nCandidate front among listed paths:\n");
+        for &index in &self.result.front {
+            let chain = fmt_path_chain(graph, &paths[index]);
+            text.push_str(&format!("  Path {}: {chain}\n", index + 1));
+            for (name, f) in &self.profiles[index].fields {
+                text.push_str(&format!("    {name} {f}\n"));
+                let certificate = f.certificate.as_ref().ok().map(|(poly, _)| poly);
+                if let Some(original) = f
+                    .original_signed
+                    .as_ref()
+                    .filter(|o| Some(*o) != certificate)
+                {
+                    text.push_str(&format!("      original signed: {}\n", original.to_expr()));
+                }
+            }
+        }
+        if proofs {
+            text.push_str(
+                "\nField proofs (forward: first path ≤O second; reverse: second ≤O first):\n",
+            );
+            for (i, j, c) in &self.result.pairs {
+                text.push_str(&format!(
+                    "  Paths {}, {}: {}\n",
+                    i + 1,
+                    j + 1,
+                    description(*i, *j, c)
+                ));
+                for (name, f) in &c.fields {
+                    for (label, d, left, right) in [
+                        ("forward", &f.forward, *i, *j),
+                        ("reverse", &f.reverse, *j, *i),
+                    ] {
+                        let formula = |index: usize| {
+                            self.profiles[index]
+                                .fields
+                                .get(name)
+                                .map_or_else(|| "missing".into(), ToString::to_string)
+                        };
+                        text.push_str(&format!(
+                            "    {name} {label} (Path {} ≤O Path {}): f {}; g {}\n",
+                            left + 1,
+                            right + 1,
+                            formula(left),
+                            formula(right)
+                        ));
+                        for line in d.to_string().lines() {
+                            text.push_str(&format!("      {line}\n"));
+                        }
+                    }
+                }
+            }
+        }
+        text
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use problemreductions::{parameters::ParameterRelation, poly_compare::FieldCertificate, Expr};
+    use std::collections::BTreeMap;
+
+    fn certificate(s: &str) -> FieldCertificate {
+        FieldCertificate::new(&Expr::parse(s), ParameterRelation::Exact)
+    }
+    fn profile(vars: &str, terms: &str) -> Profile {
+        Profile::new(BTreeMap::from([
+            ("vars".into(), certificate(vars)),
+            ("terms".into(), certificate(terms)),
+        ]))
+    }
+    fn first(view: &ComparisonView) -> String {
+        let (i, j, c) = &view.result.pairs[0];
+        description(*i, *j, c)
+    }
+
+    #[test]
+    fn polynomial_pair_descriptions_distinguish_tradeoffs_from_refutations_and_missing_proofs() {
+        let view = ComparisonView::new(vec![profile("n", "m"), profile("n^2", "1")]);
+        assert_eq!(
+            first(&view),
+            "proven incomparable — Path 1 better on vars; Path 2 better on terms"
+        );
+        let view = ComparisonView::new(vec![profile("n", "n^2-2*n"), profile("m", "n-2")]);
+        let description = first(&view);
+        assert!(
+            description.contains("proven incomparable")
+                && description.contains("vars: mutually unbounded ratios")
+        );
+        assert!(description.contains("Path 2 better on terms"));
+        let view = ComparisonView::new(vec![
+            profile("m", "1"),
+            profile("n", "1"),
+            profile("n-m", "1"),
+        ]);
+        assert_eq!(view.result.pairs[0].2.verdict, Verdict::Unknown);
+        assert!(first(&view).contains("UNRESOLVED"));
+    }
+
+    #[test]
+    fn polynomial_front_render_keeps_signed_provenance_and_unavailable_reasons() {
+        let graph = ReductionGraph::new();
+        let batch = super::super::find_path_batch(
+            &graph,
+            "MaximumIndependentSet",
+            &graph.default_variant_for("MaximumIndependentSet").unwrap(),
+            "QUBO",
+            &graph.default_variant_for("QUBO").unwrap(),
+            2,
+        )
+        .unwrap();
+        let mut left = profile("n", "n^2-m");
+        let vars = left.fields.get_mut("vars").unwrap();
+        vars.certificate = Ok((
+            problemreductions::polynomial::Poly::from_expr(&Expr::parse("n")).unwrap(),
+            ParameterRelation::UpperBound,
+        ));
+        vars.original_signed = problemreductions::polynomial::Poly::from_expr(&Expr::parse("n-m"));
+        left.fields.insert("missing".into(), certificate("log(n)"));
+        let mut right = profile("n", "n");
+        right.fields.get_mut("vars").unwrap().certificate = Ok((
+            problemreductions::polynomial::Poly::from_expr(&Expr::parse("n")).unwrap(),
+            ParameterRelation::UpperBound,
+        ));
+        let view = ComparisonView::new(vec![left, right]);
+        let text = view.render(&graph, &batch.paths, true);
+        assert!(text.contains("vars <= n\n"));
+        assert!(text.contains("original signed:") && text.contains("unavailable"));
+        assert!(text.contains("UNRESOLVED") && text.contains("missing obligation:"));
+        assert!(text.contains("not polynomial:") && text.contains("Field proofs"));
+        assert!(
+            view.to_json()["profiles"][0]["fields"]["missing"]["accuracy"]["reason"].is_object()
+        );
+    }
+}
diff --git a/problemreductions-cli/src/main.rs b/problemreductions-cli/src/main.rs
index c6aa069cc..7f2e54ac7 100644
--- a/problemreductions-cli/src/main.rs
+++ b/problemreductions-cli/src/main.rs
@@ -71,7 +71,17 @@ fn main() -> anyhow::Result<()> {
             target,
             limit,
             instance,
-        } => commands::graph::path(&source, &target, limit, instance.as_deref(), &out),
+            compare,
+            proofs,
+        } => commands::graph::path(
+            &source,
+            &target,
+            limit,
+            instance.as_deref(),
+            compare,
+            proofs,
+            &out,
+        ),
         Commands::ExportGraph => commands::graph::export(&out),
         Commands::Inspect(args) => commands::inspect::inspect(&args.input, &out),
         Commands::Create(args) => commands::create::create(&args, &out),
diff --git a/problemreductions-cli/tests/cli_tests.rs b/problemreductions-cli/tests/cli_tests.rs
index 6beade5f9..019808dde 100644
--- a/problemreductions-cli/tests/cli_tests.rs
+++ b/problemreductions-cli/tests/cli_tests.rs
@@ -25,6 +25,93 @@ fn pred() -> Command {
     Command::new(env!("CARGO_BIN_EXE_pred"))
 }
 
+#[test]
+fn path_text_preserves_variant_conversion_steps() {
+    for compare in [true, false] {
+        let mut command = pred();
+        command.args(["path", "MIS", "MIS/SimpleGraph/i64", "--limit", "1"]);
+        if compare {
+            command.arg("--compare");
+        }
+        let output = command.output().unwrap();
+        assert!(
+            output.status.success(),
+            "{}",
+            String::from_utf8_lossy(&output.stderr)
+        );
+        let text = String::from_utf8(output.stdout).unwrap();
+        assert!(
+            text.contains(
+                "MaximumIndependentSet/SimpleGraph/One → MaximumIndependentSet/SimpleGraph/i64"
+            ),
+            "{text}"
+        );
+    }
+}
+
+#[test]
+fn polynomial_comparison_default_layout_and_opt_in_proofs() {
+    let args = ["path", "MIS", "QUBO", "--compare", "--limit", "3"];
+    let output = pred().args(args).output().unwrap();
+    assert!(output.status.success());
+    let text = String::from_utf8(output.stdout).unwrap();
+    let semantics = text.find("generic order").unwrap();
+    let front = text.find("Candidate front").unwrap();
+    let pairs = text.find("Pair verdicts").unwrap();
+    let unresolved = text.find("Unresolved pairs").unwrap();
+    assert!(semantics < pairs && pairs < unresolved && unresolved < front);
+    assert!(text.contains("Path 1") && text.contains("num_vars"));
+    assert!(!text.contains("[upper bound]") && !text.contains("[exact]"));
+    assert!(text[pairs..unresolved]
+        .contains("0 dominated, 1 equivalent, 2 proven incomparable, 0 unresolved"));
+    assert!(!text.contains("worst case:") && !text.contains("Generic candidate front"));
+    assert!(text.contains("Paths 1, 2: proven incomparable"));
+    assert!(text.contains("Paths 2, 3: Path 2 ≡ Path 3"));
+    assert!(
+        text.contains("Ignores exact-cancellation families") && text.contains("bounded strata")
+    );
+    assert!(text.contains("2 proven incomparable, 0 unresolved"));
+    assert!(
+        !text.contains("Field proofs") && !text.contains("Witness {") && !text.contains("f/g → ∞")
+    );
+
+    let output = pred().args(args).arg("--proofs").output().unwrap();
+    assert!(output.status.success());
+    let text = String::from_utf8(output.stdout).unwrap();
+    assert!(
+        text.contains("Paths 1, 2: proven incomparable")
+            && text.contains("Paths 2, 3: Path 2 ≡ Path 3")
+    );
+    assert!(text.contains("Field proofs") && text.contains("f/g → ∞"));
+    assert!(text.contains("f ≡ g after expansion"));
+    assert!(text.contains("No (regular and positive across the batch)") && text.contains("Yes:"));
+
+    let output = pred().args(args).arg("--json").output().unwrap();
+    assert!(output.status.success());
+    let json: serde_json::Value = serde_json::from_slice(&output.stdout).unwrap();
+    let view = &json["polynomial_comparison"];
+    assert_eq!(view["schema_version"], 5);
+    assert_eq!(view["mode"], "generic");
+    assert_eq!(view["counts"]["Incomparable"], 2);
+    assert!(view.get("generic_counts").is_none());
+    assert!(view.get("generic_candidate_front").is_none());
+    assert!(view["pairs"][0]["fields"]["num_vars"]["forward"]["certificate"].is_object());
+    let identity = &view["pairs"][2]["fields"]["num_vars"]["forward"]["certificate"];
+    assert_eq!(identity["kind"], "identity");
+    assert_eq!(identity.as_object().unwrap().len(), 1);
+    assert!(view["pairs"][2]["fields"]["num_vars"]
+        .get("generic")
+        .is_none());
+    let output = pred()
+        .args(["path", "MIS", "QUBO", "--proofs"])
+        .output()
+        .unwrap();
+    assert!(!output.status.success());
+    assert!(String::from_utf8(output.stderr)
+        .unwrap()
+        .contains("--compare"));
+}
+
 fn extract_target_config(
     bundle: &std::path::Path,
     config: serde_json::Value,
diff --git a/problemreductions-expr/src/lib.rs b/problemreductions-expr/src/lib.rs
index 0d746b119..37ce144be 100644
--- a/problemreductions-expr/src/lib.rs
+++ b/problemreductions-expr/src/lib.rs
@@ -708,6 +708,12 @@ impl fmt::Display for SubstitutionError {
 
 impl std::error::Error for SubstitutionError {}
 
+impl std::iter::Sum for Expr {
+    fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
+        Self::add_all(iter.collect())
+    }
+}
+
 impl std::ops::Add for Expr {
     type Output = Self;
     fn add(self, rhs: Self) -> Self::Output {
diff --git a/problemreductions-web/Cargo.toml b/problemreductions-web/Cargo.toml
new file mode 100644
index 000000000..7c6365e3e
--- /dev/null
+++ b/problemreductions-web/Cargo.toml
@@ -0,0 +1,31 @@
+[package]
+name = "problemreductions-web"
+version = "0.6.0"
+edition = "2021"
+publish = false
+
+[lib]
+crate-type = ["cdylib", "rlib"]
+test = false
+doctest = false
+
+[features]
+schema-export = ["dep:schemars"]
+
+[dependencies]
+problemreductions-expr = { path = "../problemreductions-expr" }
+num-bigint = "0.4.8"
+num-rational = "0.4.2"
+num-traits = "0.2.19"
+serde = { version = "1.0.229", features = ["derive"] }
+serde_json = "1.0.151"
+thiserror = "2.0.20"
+wasm-bindgen = "=0.2.129"
+schemars = { version = "=1.2.2", optional = true }
+
+[dev-dependencies]
+proptest = "1.11.0"
+
+[[example]]
+name = "export_frontend_schema"
+required-features = ["schema-export"]
diff --git a/problemreductions-web/examples/export_frontend_schema.rs b/problemreductions-web/examples/export_frontend_schema.rs
new file mode 100644
index 000000000..bf7356d73
--- /dev/null
+++ b/problemreductions-web/examples/export_frontend_schema.rs
@@ -0,0 +1,16 @@
+//! Emit request/response schemas derived from the browser wire structs.
+use problemreductions_web::{
+    comparison_request_schema, comparison_response_schema, path_request_schema,
+    path_response_schema,
+};
+
+fn main() -> Result<(), Box<dyn std::error::Error>> {
+    let schemas = serde_json::json!({
+        "wasm-path-request": path_request_schema(),
+        "wasm-comparison-request": comparison_request_schema(),
+        "wasm-paths": path_response_schema(),
+        "wasm-comparison": comparison_response_schema(),
+    });
+    serde_json::to_writer(std::io::stdout().lock(), &schemas)?;
+    Ok(())
+}
diff --git a/problemreductions-web/src/lib.rs b/problemreductions-web/src/lib.rs
new file mode 100644
index 000000000..36eae808e
--- /dev/null
+++ b/problemreductions-web/src/lib.rs
@@ -0,0 +1,498 @@
+//! Browser bindings compile the native symbolic and path-search sources directly.
+#[path = "../../src/expr.rs"]
+pub mod expr;
+#[path = "../../src/parameters.rs"]
+pub mod parameters;
+#[path = "../../src/path_search.rs"]
+mod path_search;
+#[path = "../../src/poly_compare/mod.rs"]
+pub mod poly_compare;
+#[path = "../../src/polynomial.rs"]
+pub mod polynomial;
+#[path = "../../src/problem_parameters.rs"]
+pub mod types;
+
+use expr::{Expr, Symbol};
+use parameters::{ParameterRelation, ParameterTransform};
+use poly_compare::{compare_summary, Profile, Reason};
+use serde::{Deserialize, Serialize};
+use std::collections::BTreeMap;
+use wasm_bindgen::prelude::*;
+
+/// Largest integer a JavaScript number represents exactly.
+#[cfg(feature = "schema-export")]
+const JS_SAFE_MAX: u64 = 9_007_199_254_740_991;
+
+#[derive(Deserialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+struct Node {
+    name: String,
+    variant: BTreeMap<String, String>,
+    parameter_names: Vec<String>,
+}
+#[derive(Deserialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+struct Parameter {
+    field: String,
+    contract: Contract,
+    formula: Option<String>,
+    reason: Option<String>,
+}
+#[derive(Deserialize, PartialEq)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+#[serde(rename_all = "snake_case")]
+enum Contract {
+    Exact,
+    UpperBound,
+    Unavailable,
+}
+#[derive(Deserialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+struct Edge {
+    #[cfg_attr(feature = "schema-export", schemars(range(max = JS_SAFE_MAX)))]
+    source: usize,
+    #[cfg_attr(feature = "schema-export", schemars(range(max = JS_SAFE_MAX)))]
+    target: usize,
+    witness: bool,
+    turing: bool,
+    parameters: Vec<Parameter>,
+    parameter_contract_error: Option<String>,
+}
+#[derive(Deserialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+struct Graph {
+    nodes: Vec<Node>,
+    edges: Vec<Edge>,
+}
+#[derive(Deserialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+#[cfg_attr(feature = "schema-export", schemars(extend("$id" = "https://codingthrust.github.io/problem-reductions/contracts/wasm-path-request")))]
+struct Query {
+    graph: Graph,
+    #[cfg_attr(feature = "schema-export", schemars(range(max = JS_SAFE_MAX)))]
+    source: usize,
+    #[cfg_attr(feature = "schema-export", schemars(range(max = JS_SAFE_MAX)))]
+    target: usize,
+    #[cfg_attr(feature = "schema-export", schemars(range(min = 1, max = 999)))]
+    limit: usize,
+}
+
+#[wasm_bindgen]
+pub fn find_paths(input: &str) -> Result<String, JsError> {
+    let query: Query = serde_json::from_str(input)?;
+    let Graph { nodes, edges } = query.graph;
+    if !(1..=999).contains(&query.limit)
+        || query.source >= nodes.len()
+        || query.target >= nodes.len()
+    {
+        return Err(JsError::new(
+            "Choose registered endpoints and a path limit from 1 to 999.",
+        ));
+    }
+    let mut order: Vec<_> = (0..nodes.len()).collect();
+    order.sort_by_key(|&i| (&nodes[i].name, &nodes[i].variant));
+    let mut ranks = vec![0; nodes.len()];
+    for (rank, &i) in order.iter().enumerate() {
+        ranks[i] = rank;
+    }
+    let mut adjacency = vec![Vec::new(); nodes.len()];
+    for edge in &edges {
+        if edge.source >= nodes.len() || edge.target >= nodes.len() {
+            return Err(JsError::new(
+                "Reduction graph contains an invalid endpoint.",
+            ));
+        }
+        if edge.witness && !edge.turing {
+            adjacency[edge.source].push(edge.target);
+        }
+    }
+    for neighbors in &mut adjacency {
+        neighbors.sort_by_key(|&i| ranks[i]);
+    }
+    let mut paths = path_search::find_paths(
+        &adjacency,
+        &ranks,
+        query.source,
+        query.target,
+        query.limit + 1,
+        nodes.len(),
+    );
+    let truncated = paths.len() > query.limit;
+    paths.truncate(query.limit);
+    let endpoint = |i: usize| Endpoint {
+        name: nodes[i].name.clone(),
+        variant: nodes[i].variant.clone(),
+    };
+    let routes = paths
+        .iter()
+        .map(|path| Route {
+            steps: path.len() - 1,
+            path: path
+                .windows(2)
+                .map(|pair| Step {
+                    from: endpoint(pair[0]),
+                    to: endpoint(pair[1]),
+                })
+                .collect(),
+        })
+        .collect();
+    Ok(serde_json::to_string(&WasmPathResult {
+        paths: routes,
+        truncated,
+    })?)
+}
+
+#[derive(Deserialize, Serialize, PartialEq)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+#[cfg_attr(feature = "schema-export", schemars(deny_unknown_fields))]
+struct Endpoint {
+    #[cfg_attr(feature = "schema-export", schemars(length(min = 1)))]
+    name: String,
+    variant: BTreeMap<String, String>,
+}
+#[derive(Deserialize, Serialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+#[cfg_attr(feature = "schema-export", schemars(deny_unknown_fields))]
+struct Step {
+    from: Endpoint,
+    to: Endpoint,
+}
+#[derive(Deserialize, Serialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+#[cfg_attr(feature = "schema-export", schemars(deny_unknown_fields))]
+struct Route {
+    #[cfg_attr(
+        feature = "schema-export",
+        schemars(range(min = 1, max = JS_SAFE_MAX))
+    )]
+    steps: usize,
+    #[cfg_attr(feature = "schema-export", schemars(length(min = 1)))]
+    path: Vec<Step>,
+}
+
+#[derive(Serialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+#[cfg_attr(feature = "schema-export", schemars(deny_unknown_fields,
+    extend("$id" = "https://codingthrust.github.io/problem-reductions/contracts/wasm-paths")))]
+struct WasmPathResult {
+    #[cfg_attr(feature = "schema-export", schemars(length(max = 999)))]
+    paths: Vec<Route>,
+    truncated: bool,
+}
+
+/// Generate the browser response contract without adding schema tooling to WASM builds.
+#[cfg(feature = "schema-export")]
+pub fn path_response_schema() -> schemars::Schema {
+    wire_schema::<WasmPathResult>(
+        schemars::generate::SchemaSettings::draft2020_12().for_serialize(),
+    )
+}
+
+/// Generate the comparison response contract.
+#[cfg(feature = "schema-export")]
+pub fn comparison_response_schema() -> schemars::Schema {
+    wire_schema::<WasmComparisonResult>(
+        schemars::generate::SchemaSettings::draft2020_12().for_serialize(),
+    )
+}
+
+/// Generate the input contract from the actual native deserialization types.
+#[cfg(feature = "schema-export")]
+pub fn path_request_schema() -> schemars::Schema {
+    wire_schema::<Query>(schemars::generate::SchemaSettings::draft2020_12().for_deserialize())
+}
+
+/// Generate the input contract for `summarize_paths`.
+#[cfg(feature = "schema-export")]
+pub fn comparison_request_schema() -> schemars::Schema {
+    wire_schema::<ComparisonQuery>(
+        schemars::generate::SchemaSettings::draft2020_12().for_deserialize(),
+    )
+}
+
+#[cfg(feature = "schema-export")]
+fn wire_schema<T: schemars::JsonSchema>(
+    mut settings: schemars::generate::SchemaSettings,
+) -> schemars::Schema {
+    // JSON numeric bounds carry the domain; Rust's integer formats are nonstandard.
+    settings
+        .transforms
+        .push(Box::new(schemars::transform::RecursiveTransform(
+            |schema: &mut schemars::Schema| {
+                if matches!(
+                    schema.get("format").and_then(|value| value.as_str()),
+                    Some("uint" | "uint8")
+                ) {
+                    schema.remove("format");
+                }
+            },
+        )));
+    settings.into_generator().into_root_schema_for::<T>()
+}
+
+#[derive(Serialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+#[cfg_attr(feature = "schema-export", schemars(deny_unknown_fields,
+    extend("$id" = "https://codingthrust.github.io/problem-reductions/contracts/wasm-comparison")))]
+struct WasmComparisonResult {
+    profiles: Vec<ComparisonProfile>,
+    #[cfg_attr(
+        feature = "schema-export",
+        schemars(inner(range(min = 1, max = JS_SAFE_MAX)))
+    )]
+    front: Vec<usize>,
+    counts: ComparisonCounts,
+}
+
+#[derive(Serialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+#[cfg_attr(feature = "schema-export", schemars(deny_unknown_fields))]
+#[serde(rename_all = "PascalCase")]
+struct ComparisonCounts {
+    #[cfg_attr(feature = "schema-export", schemars(range(max = JS_SAFE_MAX)))]
+    dominated: usize,
+    #[cfg_attr(feature = "schema-export", schemars(range(max = JS_SAFE_MAX)))]
+    equivalent: usize,
+    #[cfg_attr(feature = "schema-export", schemars(range(max = JS_SAFE_MAX)))]
+    incomparable: usize,
+    #[cfg_attr(feature = "schema-export", schemars(range(max = JS_SAFE_MAX)))]
+    unknown: usize,
+}
+
+impl From<[usize; 4]> for ComparisonCounts {
+    fn from([dominated, equivalent, incomparable, unknown]: [usize; 4]) -> Self {
+        Self {
+            dominated,
+            equivalent,
+            incomparable,
+            unknown,
+        }
+    }
+}
+
+#[derive(Serialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+#[cfg_attr(feature = "schema-export", schemars(deny_unknown_fields))]
+struct ComparisonProfile {
+    #[cfg_attr(feature = "schema-export", schemars(inner(length(min = 1))))]
+    source_coordinates: Vec<String>,
+    #[cfg_attr(feature = "schema-export", schemars(extend("propertyNames" = {"type": "string", "minLength": 1})))]
+    fields: BTreeMap<String, ComparisonField>,
+}
+
+#[derive(Serialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+#[cfg_attr(feature = "schema-export", schemars(deny_unknown_fields))]
+struct ComparisonField {
+    #[cfg_attr(feature = "schema-export", schemars(length(min = 1)))]
+    certificate: Option<String>,
+    accuracy: ComparisonAccuracy,
+}
+
+#[derive(Serialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+#[cfg_attr(feature = "schema-export", schemars(deny_unknown_fields))]
+#[serde(tag = "kind", rename_all = "snake_case")]
+enum ComparisonAccuracy {
+    Exact,
+    UpperBound,
+    Unavailable { reason: ComparisonReason },
+}
+
+#[derive(Serialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+#[cfg_attr(feature = "schema-export", schemars(deny_unknown_fields))]
+#[serde(tag = "kind", rename_all = "snake_case")]
+enum ComparisonReason {
+    NotPolynomial { detail: String },
+    Unavailable { detail: String },
+    MissingField,
+    Validity,
+    ResourceLimit { detail: String },
+}
+
+impl From<&Reason> for ComparisonReason {
+    fn from(reason: &Reason) -> Self {
+        match reason {
+            Reason::NotPolynomial(detail) => Self::NotPolynomial {
+                detail: detail.clone(),
+            },
+            Reason::Unavailable(error) => Self::Unavailable {
+                detail: error.to_string(),
+            },
+            Reason::MissingField => Self::MissingField,
+            Reason::Validity => Self::Validity,
+            Reason::ResourceLimit(detail) => Self::ResourceLimit {
+                detail: (*detail).to_string(),
+            },
+        }
+    }
+}
+#[derive(Deserialize)]
+#[cfg_attr(feature = "schema-export", derive(schemars::JsonSchema))]
+#[cfg_attr(feature = "schema-export", schemars(extend("$id" = "https://codingthrust.github.io/problem-reductions/contracts/wasm-comparison-request")))]
+struct ComparisonQuery {
+    graph: Graph,
+    paths: Vec<Route>,
+}
+
+impl Graph {
+    fn route_indices(&self, route: &Route) -> Result<Vec<usize>, JsError> {
+        if route.path.is_empty() || route.steps != route.path.len() {
+            return Err(JsError::new("Choose a nonempty registered reduction path."));
+        }
+        let index = |endpoint: &Endpoint| {
+            self.nodes
+                .iter()
+                .position(|node| node.name == endpoint.name && node.variant == endpoint.variant)
+                .ok_or_else(|| JsError::new("Path references an unregistered variant."))
+        };
+        let mut indices = vec![index(&route.path[0].from)?];
+        for step in &route.path {
+            let source = index(&step.from)?;
+            let target = index(&step.to)?;
+            if indices.last() != Some(&source)
+                || !self.edges.iter().any(|edge| {
+                    edge.source == source && edge.target == target && edge.witness && !edge.turing
+                })
+            {
+                return Err(JsError::new("Path references an unregistered reduction."));
+            }
+            indices.push(target);
+        }
+        Ok(indices)
+    }
+}
+
+/// Browser result: certificates, all pair counts and the front, retaining one-based route indices.
+#[wasm_bindgen]
+pub fn summarize_paths(input: &str) -> Result<String, JsError> {
+    let query: ComparisonQuery = serde_json::from_str(input)?;
+    let Graph { nodes, edges } = &query.graph;
+    let mut profiles = Vec::new();
+    for route in query.paths {
+        let path = query.graph.route_indices(&route)?;
+        let mut composed: Option<ParameterTransform> = None;
+        for pair in path.windows(2) {
+            let edge = edges
+                .iter()
+                .find(|edge| edge.source == pair[0] && edge.target == pair[1])
+                .ok_or_else(|| JsError::new("Path references an unregistered reduction."))?;
+            if let Some(error) = &edge.parameter_contract_error {
+                return Err(JsError::new(error));
+            }
+            let mut fields = Vec::new();
+            for parameter in &edge.parameters {
+                if parameter.contract == Contract::Unavailable {
+                    continue;
+                }
+                let formula = parameter
+                    .formula
+                    .as_ref()
+                    .ok_or_else(|| JsError::new("Missing parameter formula."))?;
+                let relation = if parameter.contract == Contract::Exact {
+                    ParameterRelation::Exact
+                } else {
+                    ParameterRelation::UpperBound
+                };
+                fields.push((parameter.field.clone(), relation, Expr::try_parse(formula)?));
+            }
+            let mut transform = ParameterTransform::from_fields(
+                format!("{} -> {}", nodes[pair[0]].name, nodes[pair[1]].name),
+                fields,
+            )?;
+            for parameter in &edge.parameters {
+                if parameter.contract == Contract::Unavailable {
+                    transform.declare_unavailable(
+                        &parameter.field,
+                        parameter.reason.as_deref().ok_or_else(|| {
+                            JsError::new("Missing reason for unavailable parameter.")
+                        })?,
+                    );
+                }
+            }
+            composed = Some(if let Some(prefix) = composed {
+                prefix.compose(
+                    &transform,
+                    format!("{} -> {}", nodes[path[0]].name, nodes[pair[1]].name),
+                )?
+            } else {
+                transform
+            });
+        }
+        let mut profile =
+            Profile::from_transform(&composed.expect("validated nonempty reduction path"));
+        for field in profile.fields.values_mut() {
+            field.original_signed = None;
+        }
+        profile.domain.extend(
+            nodes[path[0]]
+                .parameter_names
+                .iter()
+                .filter_map(|name| Symbol::new(name.as_str()).ok()),
+        );
+        profiles.push(profile);
+    }
+    let result = compare_summary(&profiles);
+    let profiles = profiles
+        .iter()
+        .map(|profile| {
+            let fields = profile
+                .fields
+                .iter()
+                .map(|(name, field)| {
+                    let (certificate, accuracy) = match &field.certificate {
+                        Ok((poly, relation)) => (
+                            Some(poly.to_expr().to_string()),
+                            match relation {
+                                ParameterRelation::Exact => ComparisonAccuracy::Exact,
+                                ParameterRelation::UpperBound => ComparisonAccuracy::UpperBound,
+                            },
+                        ),
+                        Err(reason) => (
+                            None,
+                            ComparisonAccuracy::Unavailable {
+                                reason: reason.into(),
+                            },
+                        ),
+                    };
+                    (
+                        name.clone(),
+                        ComparisonField {
+                            certificate,
+                            accuracy,
+                        },
+                    )
+                })
+                .collect();
+            ComparisonProfile {
+                source_coordinates: profile.domain.iter().map(ToString::to_string).collect(),
+                fields,
+            }
+        })
+        .collect();
+    Ok(serde_json::to_string(&WasmComparisonResult {
+        profiles,
+        front: result.front.into_iter().map(|index| index + 1).collect(),
+        counts: result.counts.into(),
+    })?)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn comparison_reason_wire_format_matches_native_proof_format() {
+        for reason in [
+            Reason::MissingField,
+            Reason::Validity,
+            Reason::ResourceLimit("Exact arithmetic budget exhausted"),
+        ] {
+            assert_eq!(
+                serde_json::to_value(ComparisonReason::from(&reason)).unwrap(),
+                serde_json::to_value(reason).unwrap()
+            );
+        }
+    }
+}
diff --git a/problemreductions-web/tests/paths.rs b/problemreductions-web/tests/paths.rs
new file mode 100644
index 000000000..718a888e9
--- /dev/null
+++ b/problemreductions-web/tests/paths.rs
@@ -0,0 +1,236 @@
+use problemreductions_web::{find_paths, summarize_paths};
+use serde_json::{json, Value};
+
+fn graph() -> Value {
+    json!({
+        "nodes": [
+            {"name":"Source", "variant":{}, "parameter_names":["m", "n"]},
+            {"name":"Target", "variant":{"weight":"One"}, "parameter_names":["n"]},
+            {"name":"Target", "variant":{"weight":"i64"}, "parameter_names":["n"]}
+        ],
+        "edges": [
+            {"source":0, "target":2, "witness":true, "turing":false,
+             "parameters":[{"field":"n", "contract":"exact", "formula":"n^2"}]},
+            {"source":0, "target":1, "witness":true, "turing":false,
+             "parameters":[{"field":"n", "contract":"exact", "formula":"n"}]},
+            {"source":1, "target":2, "witness":true, "turing":false,
+             "parameters":[{"field":"n", "contract":"exact", "formula":"n"}]}
+        ]
+    })
+}
+
+#[test]
+fn paths_arrive_without_composing_or_comparing_parameter_formulas() {
+    let mut graph = graph();
+    graph["edges"][0]["parameter_contract_error"] = json!("Unavailable certificate");
+    let result: Value = serde_json::from_str(
+        &find_paths(
+            &json!({
+                "graph":graph, "source":0, "target":2, "limit":1
+            })
+            .to_string(),
+        )
+        .unwrap(),
+    )
+    .unwrap();
+    assert_eq!(
+        result,
+        json!({"truncated":true, "paths":[{
+            "steps":1, "path":[{"from":{"name":"Source", "variant":{}},
+                "to":{"name":"Target", "variant":{"weight":"i64"}}}]
+        }]})
+    );
+}
+
+#[test]
+fn comparison_ranks_the_supplied_exact_variant_routes() {
+    let graph = graph();
+    let result: Value = serde_json::from_str(
+        &find_paths(
+            &json!({
+                "graph":graph, "source":0, "target":2, "limit":20
+            })
+            .to_string(),
+        )
+        .unwrap(),
+    )
+    .unwrap();
+    assert_eq!(result["truncated"], false);
+    assert_eq!(result["paths"].as_array().unwrap().len(), 2);
+    assert_eq!(
+        result["paths"][1]["path"][0]["to"]["variant"]["weight"],
+        "One"
+    );
+    let comparison: Value = serde_json::from_str(
+        &summarize_paths(
+            &json!({
+                "graph":graph, "paths":[result["paths"][1],result["paths"][0]]
+            })
+            .to_string(),
+        )
+        .unwrap(),
+    )
+    .unwrap();
+    assert_eq!(comparison["front"], json!([1]));
+    assert_eq!(
+        comparison["profiles"][0]["source_coordinates"],
+        json!(["m", "n"])
+    );
+    assert_eq!(
+        comparison["profiles"][0]["fields"]["n"],
+        json!({
+            "certificate":"n", "accuracy":{"kind":"exact"}
+        })
+    );
+    assert_eq!(comparison["profiles"].as_array().unwrap().len(), 2);
+    assert_eq!(comparison["counts"]["Dominated"], 1);
+}
+
+#[test]
+fn browser_summary_keeps_profiles_counts_and_front_without_pair_payloads() {
+    let graph = graph();
+    let routes: Value = serde_json::from_str(
+        &find_paths(
+            &json!({
+                "graph": graph, "source": 0, "target": 2, "limit": 20
+            })
+            .to_string(),
+        )
+        .unwrap(),
+    )
+    .unwrap();
+    let input = json!({"graph": graph, "paths": routes["paths"]}).to_string();
+    let summary: Value = serde_json::from_str(&summarize_paths(&input).unwrap()).unwrap();
+    assert!(summary.get("schema_version").is_none());
+    assert!(summary.get("mode").is_none());
+    assert_eq!(
+        summary["counts"],
+        json!({"Dominated":1,"Equivalent":0,"Incomparable":0,"Unknown":0})
+    );
+    assert_eq!(summary["front"], json!([2]));
+    assert!(summary.get("pairs").is_none());
+}
+
+#[test]
+fn comparison_retains_exact_wide_rational_coefficients() {
+    use num_bigint::{BigInt, BigUint};
+    use num_rational::BigRational;
+    use problemreductions_web::{
+        expr::{Expr, Symbol},
+        polynomial::Poly,
+    };
+    use std::collections::BTreeMap;
+
+    let mut graph = graph();
+    graph["edges"] = json!([graph["edges"][0]]);
+    graph["edges"][0]["parameters"][0]["formula"] = json!("9007199254740993 / 7 * n");
+    graph["edges"][0]["parameters"][0]["contract"] = json!("upper_bound");
+    let routes: Value = serde_json::from_str(
+        &find_paths(
+            &json!({
+                "graph": graph, "source": 0, "target": 2, "limit": 1
+            })
+            .to_string(),
+        )
+        .unwrap(),
+    )
+    .unwrap();
+    let input = json!({"graph":graph, "paths":routes["paths"]}).to_string();
+    let result: Value = serde_json::from_str(&summarize_paths(&input).unwrap()).unwrap();
+    let field = &result["profiles"][0]["fields"]["n"];
+    let certificate = field["certificate"].as_str().unwrap();
+    assert_eq!(field["accuracy"]["kind"], "upper_bound");
+    let poly = Poly::from_expr(&Expr::try_parse(certificate).unwrap()).unwrap();
+    assert_eq!(
+        poly.terms(),
+        &BTreeMap::from([(
+            BTreeMap::from([(Symbol::new("n").unwrap(), BigUint::from(1u8))]),
+            BigRational::new(BigInt::from(9007199254740993u64), BigInt::from(7u8))
+        )])
+    );
+    assert!(result.get("pairs").is_none());
+}
+
+#[test]
+fn comparison_retains_explicit_null_certificates_and_typed_unavailable_reasons() {
+    for (parameter, expected_reason) in [
+        (
+            json!({"field":"n", "contract":"unavailable", "reason":"Target count is not certified"}),
+            "unavailable",
+        ),
+        (
+            json!({"field":"n", "contract":"exact", "formula":"n^-1"}),
+            "not_polynomial",
+        ),
+    ] {
+        let mut graph = graph();
+        graph["edges"] = json!([graph["edges"][0]]);
+        graph["edges"][0]["parameters"] = json!([parameter]);
+        let routes: Value = serde_json::from_str(
+            &find_paths(
+                &json!({
+                    "graph":graph, "source":0, "target":2, "limit":1
+                })
+                .to_string(),
+            )
+            .unwrap(),
+        )
+        .unwrap();
+        let result: Value = serde_json::from_str(
+            &summarize_paths(
+                &json!({
+                    "graph":graph, "paths":routes["paths"]
+                })
+                .to_string(),
+            )
+            .unwrap(),
+        )
+        .unwrap();
+        let field = &result["profiles"][0]["fields"]["n"];
+        assert_eq!(field.get("certificate"), Some(&Value::Null));
+        assert_eq!(field["accuracy"]["kind"], "unavailable");
+        assert_eq!(field["accuracy"]["reason"]["kind"], expected_reason);
+        assert!(field["accuracy"]["reason"]["detail"]
+            .as_str()
+            .is_some_and(|detail| !detail.is_empty()));
+    }
+}
+
+#[test]
+fn nondominated_comparisons_keep_both_routes() {
+    for (formula, verdict) in [
+        ("n", "Equivalent"),
+        ("m", "Incomparable"),
+        ("n^-1", "Unknown"),
+    ] {
+        let mut graph = graph();
+        graph["edges"][0]["parameters"][0]["formula"] = json!(formula);
+        let routes: Value = serde_json::from_str(
+            &find_paths(&json!({"graph":graph, "source":0, "target":2, "limit":20}).to_string())
+                .unwrap(),
+        )
+        .unwrap();
+        let input = json!({"graph":graph, "paths":routes["paths"]}).to_string();
+        let summary: Value = serde_json::from_str(&summarize_paths(&input).unwrap()).unwrap();
+        assert_eq!(summary["front"], json!([1, 2]));
+        assert_eq!(summary["counts"][verdict], 1);
+        assert!(summary.get("pairs").is_none());
+    }
+}
+
+#[test]
+fn unreachable_and_identical_endpoints_have_no_routes() {
+    for (source, target) in [(2, 0), (0, 0)] {
+        let result: Value = serde_json::from_str(
+            &find_paths(
+                &json!({
+                    "graph":graph(), "source":source, "target":target, "limit":20
+                })
+                .to_string(),
+            )
+            .unwrap(),
+        )
+        .unwrap();
+        assert_eq!(result, json!({"paths":[],"truncated":false}));
+    }
+}
diff --git a/scripts/build_frontend.mjs b/scripts/build_frontend.mjs
new file mode 100644
index 000000000..d0c254a8f
--- /dev/null
+++ b/scripts/build_frontend.mjs
@@ -0,0 +1,52 @@
+import { resolve } from 'node:path';
+import { gzipSync } from 'node:zlib';
+import { build } from 'vite';
+
+const [source, destination] = process.argv.slice(2);
+if (!source || !destination) throw new Error('Usage: node scripts/build_frontend.mjs SOURCE OUTPUT');
+const output = {
+  entryFileNames: 'assets/[name].js',
+  chunkFileNames: 'assets/[name].js',
+  assetFileNames: 'assets/[name][extname]',
+};
+
+await build({
+  configFile: false,
+  root: resolve(source),
+  publicDir: false,
+  base: './',
+  plugins: [{
+    name: 'javascript-size-budget',
+    generateBundle(_options, bundle) {
+      const scripts = Object.values(bundle).filter(item => item.fileName.endsWith('.js'))
+        .map(item => Buffer.from(item.type === 'chunk' ? item.code : item.source));
+      const raw = scripts.reduce((sum, bytes) => sum + bytes.length, 0);
+      const gzip = scripts.reduce((sum, bytes) => sum + gzipSync(bytes).length, 0);
+      if (raw > 320_000 || gzip > 60_000) this.error(`JavaScript size budget exceeded: ${raw} raw / ${gzip} gzip bytes`);
+    },
+  }],
+  build: {
+    outDir: resolve(destination),
+    emptyOutDir: false,
+    assetsInlineLimit: 0,
+    // Keep the existing CSS rendering exact during the build migration.
+    cssMinify: false,
+    modulePreload: { polyfill: false },
+    // The immutable release directory supplies versioning after URL rewriting.
+    rolldownOptions: { input: ['index.html', 'graph.html'].map(name => resolve(source, name)), output,
+    },
+  },
+  worker: {
+    format: 'es',
+    // Keep the generated WASM binding/API intact beside the worker.
+    plugins: () => [{
+      name: 'preserve-wasm-binding',
+      enforce: 'pre',
+      resolveId(id) {
+        if (id === './path-selection.js') return { id, external: true };
+      },
+    }],
+    rolldownOptions: { output,
+    },
+  },
+});
diff --git a/scripts/build_graph_details.py b/scripts/build_graph_details.py
index 30a453e17..bddcbfe9a 100644
--- a/scripts/build_graph_details.py
+++ b/scripts/build_graph_details.py
@@ -122,8 +122,11 @@ def build_details(output):
         path.write_text(content)
         entries[key] = "./assets/" + quote(relative.as_posix(), safe="/")
         total_bytes += path.stat().st_size
-    (output / "graph-details.json").write_text(
-        json.dumps({"entries": entries, "anchors": parser.anchors}, ensure_ascii=True))
+    index = json.dumps({"entries": entries, "anchors": parser.anchors}, ensure_ascii=True)
+    subprocess.run(['node', str(ROOT / 'scripts/validate_website_data.mjs'), 'graph-details',
+                    (output.resolve().parent / 'index.html').as_uri(), (output.resolve() / 'details').as_uri() + '/'],
+                   input=index, text=True, check=True)
+    (output / "graph-details.json").write_text(index)
     print(f"Built {len(entries)} detail files in {time.monotonic() - started:.1f}s: "
           f"{original_bytes / 1e6:.1f} MB → {total_bytes / 1e6:.1f} MB; "
           f"index {(output / 'graph-details.json').stat().st_size / 1e3:.1f} KB")
diff --git a/scripts/build_website.py b/scripts/build_website.py
index 66ef2326b..dbfa1ad63 100644
--- a/scripts/build_website.py
+++ b/scripts/build_website.py
@@ -3,12 +3,14 @@
 
 import argparse
 import ast
+import gzip
 from html import escape
 import json
 from pathlib import Path
 import re
 import shutil
 import subprocess
+import tempfile
 import xml.etree.ElementTree as ET
 from build_graph_details import build_details
 from finalize_website import finalize
@@ -17,6 +19,20 @@
 ROOT = Path(__file__).resolve().parents[1]
 
 
+def build_frontend(output, counts, summary):
+    with tempfile.TemporaryDirectory(prefix='problem-reductions-frontend-') as directory:
+        staged = Path(directory)
+        shutil.copytree(ROOT / 'docs/website/src', staged / 'src')
+        shutil.copytree(output / 'assets', staged / 'assets')
+        (staged / 'assets/home-data.js').write_text("window.REDUCTIONS = " + json.dumps(summary, separators=(",", ":")) + ";\n")
+        for filename in ('index.html', 'graph.html'):
+            html = (ROOT / 'docs/website' / filename).read_text()
+            for key, value in counts.items():
+                html = html.replace(f"__{key}__", str(value))
+            (staged / filename).write_text(html)
+        subprocess.run(['node', str(ROOT / 'scripts/build_frontend.mjs'), str(staged), str(output)], check=True)
+
+
 def expression_mathml(expression):
     """Typeset registry arithmetic with the browser's native MathML renderer."""
     def render(node, parent_precedence=0):
@@ -124,34 +140,42 @@ def publish_open_questions(source, output):
     (output / "registry.json").write_bytes(registry)
 
 
+def build_problem_records(output, nodes, edges, schemas):
+    output.mkdir(parents=True, exist_ok=True)
+    records = []
+    for schema in schemas:
+        own = {i for i, node in enumerate(nodes) if node['name'] == schema['name']}
+        incident = [edge for edge in edges if edge['source'] in own or edge['target'] in own]
+        selected = sorted(own | {edge[end] for edge in incident for end in ('source', 'target')})
+        indices = {old: new for new, old in enumerate(selected)}
+        record = {'kind': 'record', 'nodes': [nodes[i] for i in selected],
+                  'edges': [{**edge, 'source': indices[edge['source']], 'target': indices[edge['target']]}
+                            for edge in incident],
+                  'schemas': [schema]}
+        records.append(record)
+    subprocess.run(['node', str(ROOT / 'scripts/validate_website_data.mjs'), 'atlas-records'],
+                   input=json.dumps(records), text=True, check=True)
+    for record in records:
+        (output / (record['schemas'][0]['name'] + '.json')).write_text(json.dumps(record, separators=(',', ':')))
+
+
 def build(output, graph_path, schemas_path, open_questions=None):
+    subprocess.run(['npm', 'run', 'generate:frontend-contracts'], cwd=ROOT, check=True)
     graph = json.loads(graph_path.read_text())
     schemas = json.loads(schemas_path.read_text())
+    subprocess.run(['node', str(ROOT / 'scripts/validate_website_data.mjs'), 'native-exports'],
+                   input=json.dumps({'graph': graph, 'schemas': schemas}), text=True, check=True)
     nodes, edges = graph["nodes"], graph["edges"]
-    if not nodes or any(
-        not 0 <= edge[end] < len(nodes)
-        for edge in edges
-        for end in ("source", "target")
-    ):
-        raise ValueError("The atlas requires nodes and valid edge endpoints")
     source = ROOT / "docs/website"
     output.mkdir(parents=True, exist_ok=True)
     # Replace the board on rebuild before finalizing the main site's assets.
     if (output / "open-questions").exists():
         shutil.rmtree(output / "open-questions")
     shutil.copytree(source / "assets", output / "assets", dirs_exist_ok=True)
-    shutil.copyfile(ROOT / "node_modules/cytoscape/dist/cytoscape.min.js", output / "assets/cytoscape.min.js")
-    shutil.copyfile(ROOT / "node_modules/cytoscape/LICENSE", output / "assets/cytoscape.LICENSE")
     for name in ("sat", "qubo"):
         subprocess.run(["typst", "compile", str(source / "formulas" / f"{name}.typ"),
                         str(output / "assets" / f"{name}.svg")], check=True)
     build_details(output / "assets")
-    for library in ("layout-base", "cose-base", "cytoscape-fcose"):
-        shutil.copyfile(ROOT / "node_modules" / library / "LICENSE",
-                        output / "assets" / f"{library}.LICENSE")
-    (output / "assets/layout-bundle.js").write_text(";\n".join(
-        (ROOT / "node_modules" / library / f"{library}.js").read_text()
-        for library in ("layout-base", "cose-base", "cytoscape-fcose")))
     build_markdown(output)
     # Preserve the original artwork, adapting only its colors for the dark website.
     logo = ET.parse(ROOT / "docs/logo.svg")
@@ -181,11 +205,6 @@ def build(output, graph_path, schemas_path, open_questions=None):
         "VARIANT_COUNT": len(nodes),
         "RULE_COUNT": len(edges),
     }
-    for filename in ("index.html", "graph.html"):
-        html = (source / filename).read_text()
-        for key, value in counts.items():
-            html = html.replace(f"__{key}__", str(value))
-        (output / filename).write_text(html)
     # Some cast rules are covered by shared suites rather than a dedicated file.
     # Only publish direct test links when the file actually exists.
     site_edges = []
@@ -233,18 +252,37 @@ def build(output, graph_path, schemas_path, open_questions=None):
     layout = json.loads(subprocess.run(
         ["node", str(ROOT / "scripts/generate_website_graph_layout.js"), str(graph_path)],
         check=True, capture_output=True, text=True).stdout)
-    payload = json.dumps({**graph, "layout": layout, "nodes": site_nodes,
-                         "edges": site_edges, "schemas": schemas},
-                         ensure_ascii=True)
-    (output / "assets/atlas-data.json").write_text(payload)
+    build_problem_records(output / "assets/problem-data", site_nodes, site_edges, schemas)
     summary = {
+        "kind": "summary",
         "nodes": [{key: node[key] for key in ("name", "category", "variant")} for node in nodes],
         "edges": [{key: edge[key] for key in ("source", "target")} for edge in edges],
         "schemas": [{key: schema[key] for key in ("name", "description")} for schema in schemas],
     }
-    (output / "assets/home-data.js").write_text("window.REDUCTIONS = " + json.dumps(summary, separators=(",", ":")) + ";\n")
-    (output / "assets/graph-data.js").write_text("window.REDUCTIONS = " + json.dumps(
-        {**summary, "layout": layout}, separators=(",", ":")) + ";\n")
+    subprocess.run(['node', str(ROOT / 'scripts/validate_website_data.mjs'), 'atlas-summary'],
+                   input=json.dumps(summary), text=True, check=True)
+    scene = {"layout": layout, "aliases": graph["aliases"],
+             "edges": [{key: edge[key] for key in ("source", "target", "witness", "turing")} for edge in edges],
+             "nodes": [{key: node[key] for key in ("name", "category", "variant", "default")} for node in nodes]}
+    engine = {"nodes": [{key: node[key] for key in ("name", "variant", "default", "parameter_names")} for node in nodes],
+              "edges": [{key: edge[key] for key in ('source', 'target', 'parameters', 'parameter_contract_error', 'witness', 'turing')}
+                        for edge in edges]}
+    for name, data in (("graph-scene", scene), ("path-graph", engine)):
+        subprocess.run(['node', str(ROOT / 'scripts/validate_website_data.mjs'), name],
+                       input=json.dumps(data), text=True, check=True)
+        # Portable compression also works on static preview servers without Content-Encoding.
+        (output / f"assets/{name}.json.gz").write_bytes(gzip.compress(
+            json.dumps(data, separators=(",", ":")).encode(), mtime=0))
+    # Size-optimized for the browser only: the CLI and tests keep the workspace release profile. The path search
+    # runs at the same speed; only the comparison summary is slower, and it already follows the first routes.
+    subprocess.run(["cargo", "build", "--profile", "wasm-release", "--target", "wasm32-unknown-unknown",
+                    "-p", "problemreductions-web"], cwd=ROOT, check=True)
+    subprocess.run(["wasm-bindgen", "--no-typescript", "--target", "web", "--out-name", "path-selection",
+                    "--out-dir", str(output / "assets"),
+                    str(ROOT / "target/wasm32-unknown-unknown/wasm-release/problemreductions_web.wasm")], check=True)
+    wasm = output / "assets/path-selection_bg.wasm"
+    wasm.with_suffix('.wasm.gz').write_bytes(gzip.compress(wasm.read_bytes(), mtime=0))
+    build_frontend(output, counts, summary)
     finalize(output)
     if open_questions is not None:
         publish_open_questions(open_questions, output / "open-questions")
diff --git a/scripts/check_website.py b/scripts/check_website.py
new file mode 100644
index 000000000..799b0e828
--- /dev/null
+++ b/scripts/check_website.py
@@ -0,0 +1,245 @@
+#!/usr/bin/env python3
+"""Build a fresh production website, verify it, and retain artifact provenance.
+
+uv run --no-project --with playwright==1.58.0 python scripts/check_website.py
+Use --site to verify an already assembled deployment artifact without rebuilding.
+"""
+
+import argparse
+from contextlib import contextmanager
+from functools import partial
+import hashlib
+from http.server import SimpleHTTPRequestHandler, ThreadingHTTPServer
+from importlib.metadata import version
+import json
+import os
+from pathlib import Path
+import platform
+import shutil
+import subprocess
+import sys
+import tempfile
+from threading import Thread
+
+ROOT = Path(__file__).resolve().parents[1]
+
+
+def file_digest(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def tool_path(environment):
+    current = environment.get("PATH", "")
+    cargo_bin = str(Path(environment.get("CARGO_HOME") or Path.home() / ".cargo") / "bin")
+    if cargo_bin in current.split(os.pathsep):
+        return current
+    return os.pathsep.join(part for part in [current, cargo_bin] if part)
+
+
+class PreviewServer(ThreadingHTTPServer):
+    # The cold asset burst exceeds the default accept queue on some Python versions.
+    request_queue_size = 128
+
+
+class Handler(SimpleHTTPRequestHandler):
+    def handle(self):
+        try:
+            super().handle()
+        except (BrokenPipeError, ConnectionResetError):
+            pass  # Browser navigation and worker cancellation can abandon an asset response.
+
+    def log_message(self, *args):
+        pass
+
+
+def prepare_output(path=None):
+    if path is None:
+        return Path(tempfile.mkdtemp(prefix="problem-reductions-website-"))
+    path = path.resolve()
+    path.mkdir(parents=True)
+    return path
+
+
+@contextmanager
+def serve_website(site):
+    handler = partial(Handler, directory=str(site))
+    with PreviewServer(("127.0.0.1", 0), handler) as server:
+        thread = Thread(target=server.serve_forever, daemon=True)
+        thread.start()
+        try:
+            yield f"http://127.0.0.1:{server.server_port}/"
+        finally:
+            server.shutdown()
+            thread.join()
+
+
+def source_state(root=ROOT, output=None):
+    def git(*args):
+        return subprocess.check_output(["git", *args], cwd=root)
+
+    paths = ["--", "."]
+    if output is not None and output.resolve().is_relative_to(root.resolve()):
+        paths.append(":(exclude,literal)" + output.resolve().relative_to(root.resolve()).as_posix())
+    untracked = [name for name in git("ls-files", "--others", "--exclude-standard", "-z", *paths).decode().split("\0") if name]
+    nested = {}
+    for name in untracked:
+        if (root / name).is_dir():
+            revision = subprocess.run(["git", "-C", str(root / name), "rev-parse", "--verify", "HEAD"],
+                                      capture_output=True, text=True)
+            nested[name] = revision.stdout.strip() if revision.returncode == 0 else None
+    return {
+        "revision": git("rev-parse", "HEAD").decode().strip(),
+        "working_tree_status": git("status", "--porcelain", *paths).decode(),
+        "working_tree_diff_sha256": hashlib.sha256(git("diff", "--binary", "HEAD", *paths)).hexdigest(),
+        "untracked_source": {name: file_digest(root / name)
+                             for name in untracked if (root / name).is_file()},
+        "nested_checkouts": nested,
+    }
+
+
+def verify_source_unchanged(expected, root=ROOT, output=None):
+    if source_state(root, output) != expected:
+        raise ValueError("Source checkout changed during verification; retry after edits and commits are finished")
+
+
+def write_provenance(site, verification, *, source=None):
+    tools = {"python": sys.version, **{name: version(name) for name in
+             ["playwright", "pyee", "greenlet", "typing_extensions"]}}
+    for command in ["git", "cargo", "rustc", "node", "npm", "mdbook", "typst", "wasm-bindgen"]:
+        tools[command] = subprocess.check_output([command, "--version"], text=True).strip() if shutil.which(command) else None
+    evidence = {
+        **(source if source is not None else source_state(output=site)),
+        "lockfiles": {name: file_digest(ROOT / name) for name in
+                      ["Cargo.lock", "package-lock.json", "scripts/uv.lock", "scripts/website-requirements.txt"]
+                      if (ROOT / name).is_file()},
+        "platform": platform.platform(), "tools": tools, "verification": verification,
+        "github_runner": {"image": os.environ.get("ImageOS"), "image_version": os.environ.get("ImageVersion")},
+        "artifacts": {path.relative_to(site).as_posix(): file_digest(path)
+                      for path in sorted(site.rglob("*")) if path.is_file() and path != site / "verification.json"},
+    }
+    (site / "verification.json").write_text(json.dumps(evidence, indent=2) + "\n")
+    return evidence
+
+
+def verified_artifact(site):
+    report = json.loads((site / "verification.json").read_text())
+    if report.get("verification", {}).get("status") != "passed" or not report.get("artifacts"):
+        raise ValueError("Use a production artifact with passed verification and artifact hashes")
+    for name, expected in report["artifacts"].items():
+        path = site / name
+        if not path.resolve().is_relative_to(site.resolve()):
+            raise ValueError(f"Artifact path leaves the verified directory: {name}")
+        if not path.is_file() or file_digest(path) != expected:
+            raise ValueError(f"Artifact changed or missing since verification: {name}")
+    return report
+
+
+def check(site, *, build, open_questions):
+    verification = {"status": "failed", "commands": [],
+                    "mode": "fresh_build" if build else "existing_artifact",
+                    "source_role": "build_and_verifier" if build else "verifier_only"}
+    source = source_state(output=site)
+    log = tempfile.TemporaryFile(mode="w+")
+
+    def run(command, **kwargs):
+        verification["commands"].append(command)
+        print("Running:", command, flush=True)
+        log.write(f"\nRunning: {command}\n")
+        log.flush()
+        try:
+            subprocess.run(command, cwd=ROOT, check=True, stdout=log, stderr=subprocess.STDOUT, **kwargs)
+        except subprocess.CalledProcessError:
+            log.seek(0)
+            print("".join(log.readlines()[-40:]), file=sys.stderr)
+            raise
+
+    try:
+        if build:
+            run(["npm", "ci"])
+        run(["cargo", "test", "--locked", "-p", "problemreductions-web", "--features", "schema-export", "--test", "paths"])
+        run(["npm", "run", "test:frontend-contracts"])
+        run(["npm", "run", "typecheck"])
+        run(["npm", "run", "lint:frontend"])
+        if build:
+            run(["make", "website-data"])
+            run(["mdbook", "build", "--dest-dir", str(site)])
+            run(["typst", "compile", "--root", ".", "docs/paper/reductions.typ", str(site / "reductions.pdf")])
+            run(["cargo", "doc", "--no-deps"], env={**os.environ, "RUSTDOCFLAGS": "--default-theme=dark"})
+            shutil.copytree(ROOT / "target/doc", site / "api")
+            command = [sys.executable, "scripts/build_website.py", "--output", str(site)]
+            if open_questions is not None:
+                command += ["--open-questions", str(open_questions)]
+            run(command)
+        for name in ["index.html", "graph.html", "introduction.html", "reductions.pdf", "api/problemreductions/index.html"]:
+            if not (site / name).is_file():
+                raise FileNotFoundError(f"Incomplete production artifact: {site / name}")
+        run(["npm", "run", "test:reduction-graph-js"])
+        for pattern in ["test_website_build.py", "test_website_math.py", "test_website_verification.py"]:
+            run([sys.executable, "-m", "unittest", "discover", "-s", "scripts", "-p", pattern, "--durations", "5", "-v"])
+        with serve_website(site) as base:
+            environment = {**os.environ, "WEBSITE_BASE_URL": base}
+            verification["browser_checks"] = {"root": [], "nested": [], "failure_recovery": []}
+            for engine in ["chromium", "firefox", "webkit"]:
+                run([sys.executable, "scripts/test_website.py", "--durations", "5"],
+                    env={**environment, "WEBSITE_BROWSER": engine})
+                verification["browser_checks"]["root"].append(engine)
+                run([sys.executable, "scripts/test_website_failures.py", "--durations", "5", "-v"],
+                    env={**environment, "WEBSITE_BROWSER": engine, "WEBSITE_SITE_DIR": str(site.resolve())})
+                verification["browser_checks"]["failure_recovery"].append(engine)
+        with tempfile.TemporaryDirectory(prefix="problem-reductions-nested-") as directory:
+            root = Path(directory)
+            (root / "research").mkdir()
+            (root / "research/reductions").symlink_to(site.resolve(), target_is_directory=True)
+            with serve_website(root) as base:
+                cases = ["test_alias_search_and_reset", "test_large_resources_load_only_when_needed",
+                         "test_graph_path_route_copy_solves_and_unreachable_query_is_explicit",
+                         "test_graph_details_load_lazily_reuse_family_article_and_preserve_atlas_variant",
+                         "test_reduction_evidence_and_typst_proof", "test_published_documentation_resources_and_csp"]
+                for engine in ["chromium", "firefox", "webkit"]:
+                    run([sys.executable, "scripts/test_website.py", "--durations", "5", *["WebsiteTests." + name for name in cases]],
+                        env={**os.environ, "WEBSITE_BASE_URL": base + "research/reductions/", "WEBSITE_BROWSER": engine})
+                    verification["browser_checks"]["nested"].append(engine)
+        verification["source_unchanged"] = False
+        verify_source_unchanged(source, output=site)
+        verification["source_unchanged"] = True
+        verification["status"] = "passed"
+    finally:
+        log.seek(0)
+        (site / "verification.log").write_text(log.read())
+        log.close()
+        write_provenance(site, verification, source=source)
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    mode = parser.add_mutually_exclusive_group()
+    mode.add_argument("--output", type=Path, help="Fresh output directory; existing paths are refused")
+    mode.add_argument("--site", type=Path, help="Verify an existing complete production artifact")
+    parser.add_argument("--open-questions", type=Path, help="Built Open Question Board directory to include")
+    args = parser.parse_args()
+    if args.site and args.open_questions:
+        parser.error("--open-questions applies to fresh builds; --site verifies the existing artifact")
+    os.environ["PATH"] = tool_path(os.environ)
+    tools = ["git", "node", "npm", "cargo", "rustc"]
+    if args.site is None:
+        tools += ["make", "bash", "python3", "mdbook", "typst", "wasm-bindgen"]
+    missing = [command for command in tools if shutil.which(command) is None]
+    if missing:
+        parser.error(f"Missing required tools: {', '.join(missing)}. "
+                     "Install them before retrying; see docs/website/README.md.")
+    try:
+        site = args.site.resolve() if args.site else prepare_output(args.output)
+        if not site.is_dir():
+            raise FileNotFoundError(site)
+    except OSError as error:
+        parser.exit(2, f"{error}\nUse a new --output path or --site for an existing artifact.\n")
+    print(f"Verification artifact: {site}", flush=True)
+    try:
+        check(site, build=args.site is None, open_questions=args.open_questions)
+    except ValueError as error:
+        parser.exit(1, f"{error}\nArtifact and provenance retained: {site}\n")
+    print(f"Verified artifact and provenance: {site}")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/finalize_website.py b/scripts/finalize_website.py
index 0144b9ce3..27312f400 100644
--- a/scripts/finalize_website.py
+++ b/scripts/finalize_website.py
@@ -8,7 +8,7 @@
 def finalize(output):
     release = f"releases/{time.time_ns()}"
     policy = (
-        "default-src 'self'; script-src 'self'; style-src 'self' 'unsafe-inline'; "
+        "default-src 'self'; script-src 'self' 'wasm-unsafe-eval'; style-src 'self' 'unsafe-inline'; "
         "img-src 'self' data:; font-src 'self'; connect-src 'self'; "
         "frame-src 'self'; object-src 'none'; base-uri 'self'; form-action 'none'"
     )
@@ -37,8 +37,13 @@ def externalize(match):
             return f'<script{attrs} src="{root}{target.as_posix()}"></script>'
 
         html = re.sub(r"<script\b([^>]*)>(.*?)</script>", externalize, html, flags=re.S)
-        html = re.sub(r'((?:src|href)="[^"?#]+\.(?:js|css))"',
-                      lambda m: m[1] + f'?release={release.split("/")[1]}"', html)
+        def version_resource(match):
+            # These assets move into the immutable release; imports and preloads must use the same URL.
+            if re.search(r"(?<=[\"'/])assets/", match[1]):
+                return match[0]
+            return match[1] + f'?release={release.split("/")[1]}"'
+
+        html = re.sub(r'((?:src|href)="[^"?#]+\.(?:js|css))"', version_resource, html)
         html = re.sub(r"(<head\b[^>]*>)", lambda m: m[0] +
                       f'<meta http-equiv="Content-Security-Policy" content="{policy}">', html, count=1)
         page.write_text(html)
diff --git a/scripts/generate_reduction_graph_layout.js b/scripts/generate_reduction_graph_layout.js
index 30843ec11..551b0c28d 100644
--- a/scripts/generate_reduction_graph_layout.js
+++ b/scripts/generate_reduction_graph_layout.js
@@ -53,8 +53,6 @@ function buildElkGraph(model) {
       "elk.algorithm": "stress",
       "elk.stress.desiredEdgeLength": String(STRESS_PARAMS.desiredEdgeLength),
       "elk.spacing.nodeNode": String(STRESS_PARAMS.nodeNodeSpacing),
-      // cytoscape-elk accepts this shorter key; keep it for parity with the old browser config.
-      "nodeNode.spacing": String(STRESS_PARAMS.nodeNodeSpacing),
     },
     children: nodeElements.map((element) => {
       const size = nodeSize(element);
diff --git a/scripts/generate_website_contracts.mjs b/scripts/generate_website_contracts.mjs
new file mode 100644
index 000000000..5f14727f1
--- /dev/null
+++ b/scripts/generate_website_contracts.mjs
@@ -0,0 +1,23 @@
+import { mkdir, readFile, writeFile } from 'node:fs/promises';
+import { compile } from 'json-schema-to-typescript';
+
+const root = new URL('../docs/website/', import.meta.url);
+const output = new URL('src/generated/', root);
+let input = '';
+process.stdin.setEncoding('utf8');
+for await (const chunk of process.stdin) input += chunk;
+const wasmSchemas = JSON.parse(input);
+await mkdir(output, { recursive: true });
+await writeFile(new URL('wasm-schemas.json', output), JSON.stringify(wasmSchemas));
+const schemas = { ...wasmSchemas };
+for (const name of ['atlas-data', 'graph-details', 'graph-scene', 'native-exports', 'path-graph']) {
+  schemas[name] = JSON.parse(await readFile(new URL(name + '.schema.json', root), 'utf8'));
+}
+for (const [name, schema] of Object.entries(schemas)) {
+  const types = await compile(schema, schema.title, {
+    bannerComment: '/* Generated by scripts/generate_website_contracts.mjs; do not edit. */',
+    unknownAny: true,
+    additionalProperties: false,
+  });
+  await writeFile(new URL(name + '.d.mts', output), types);
+}
diff --git a/scripts/generate_website_graph_layout.js b/scripts/generate_website_graph_layout.js
index 03840a5bf..ffcfb4087 100644
--- a/scripts/generate_website_graph_layout.js
+++ b/scripts/generate_website_graph_layout.js
@@ -1,7 +1,7 @@
 const fs = require("node:fs");
 const cytoscape = require("cytoscape");
 cytoscape.use(require("cytoscape-fcose"));
-const options = require("../docs/website/assets/graph-layout.js");
+const options = require("../docs/website/src/lib/graph-layout.js");
 const { createReductionGraphModel } = require("../docs/src/static/reduction-graph.js");
 const graph = JSON.parse(fs.readFileSync(process.argv[2], "utf8"));
 const model = createReductionGraphModel(graph);
@@ -28,5 +28,29 @@ for (const [name, id] of Object.entries(model.problemNodeIds)) {
   if (!Number.isFinite(x) || !Number.isFinite(y)) throw new Error(`Invalid position: ${name}`);
   positions[name] = bounds.h > bounds.w ? { x: y, y: -x } : { x, y };
 }
+// Publish the same overlap-adjusted positions once, instead of recomputing on every visit.
+const names = [...new Set(graph.nodes.map(node => node.name))];
+const neighbors = new Map(names.map(name => [name, new Set()]));
+for (const edge of graph.edges) {
+  const a = graph.nodes[edge.source].name, b = graph.nodes[edge.target].name;
+  if (a !== b) { neighbors.get(a).add(b); neighbors.get(b).add(a); }
+}
+const radii = names.map(name => Math.max(6, Math.min(22, 6 + 2.4 * Math.sqrt(neighbors.get(name).size))) / 2 + 9);
+for (const p of Object.values(positions)) { p.x *= 1.6; p.y *= 1.6; }
+for (let iteration = 0; iteration < 80; iteration++) {
+  let moved = false;
+  for (let i = 0; i < names.length; i++) for (let j = i + 1; j < names.length; j++) {
+    const a = positions[names[i]], b = positions[names[j]];
+    const dx = b.x - a.x, dy = b.y - a.y, distance = Math.hypot(dx, dy) || 0.01;
+    const minimum = radii[i] + radii[j];
+    if (distance < minimum) {
+      const push = (minimum - distance) / 2 / distance;
+      a.x -= dx * push; a.y -= dy * push; b.x += dx * push; b.y += dy * push;
+      moved = true;
+    }
+  }
+  if (!moved) break;
+}
+for (const p of Object.values(positions)) { p.x /= 1.6; p.y /= 1.6; }
 process.stdout.write(JSON.stringify(positions));
 cy.destroy();
diff --git a/scripts/test_website.py b/scripts/test_website.py
index cd9d2adf1..9cb771450 100644
--- a/scripts/test_website.py
+++ b/scripts/test_website.py
@@ -3,7 +3,13 @@
 
 import os
 import re
+import json
+import gzip
+from pathlib import Path
+import subprocess
+import sys
 import unittest
+import xml.etree.ElementTree as ET
 from urllib.parse import urljoin
 
 from playwright.sync_api import sync_playwright, expect
@@ -13,9 +19,14 @@ class WebsiteTests(unittest.TestCase):
     @classmethod
     def setUpClass(cls):
         cls.playwright = sync_playwright().start()
-        cls.browser = cls.playwright.chromium.launch(
-            channel=os.environ.get("WEBSITE_BROWSER_CHANNEL") or None
-        )
+        engine = os.environ.get('WEBSITE_BROWSER', 'chromium')
+        if engine not in ['chromium', 'firefox', 'webkit']:
+            raise ValueError('WEBSITE_BROWSER must be chromium, firefox or webkit')
+        options = {'channel': os.environ.get('WEBSITE_BROWSER_CHANNEL') or None} if engine == 'chromium' else {}
+        if engine == 'firefox':
+            options['firefox_user_prefs'] = {'network.proxy.type': 0}
+        cls.browser = getattr(cls.playwright, engine).launch(**options)
+        print('Website browser:', engine, cls.browser.version, flush=True)
         cls.base = os.environ.get("WEBSITE_BASE_URL", "http://127.0.0.1:3001/")
 
     @classmethod
@@ -27,7 +38,7 @@ def setUp(self):
         self.context = self.browser.new_context(
             viewport={"width": 1440, "height": 1000},
             reduced_motion="reduce",
-            permissions=["clipboard-read", "clipboard-write"],
+            permissions=["clipboard-read", "clipboard-write"] if self.browser.browser_type.name == 'chromium' else [],
         )
         self.page = self.context.new_page()
         self.page.set_default_timeout(3000)
@@ -41,6 +52,181 @@ def tearDown(self):
     def visit(self, route="home"):
         self.page.goto(self.base + "#" + route)
 
+    def scene_data(self):
+        url = urljoin(self.page.url, self.page.locator('body').get_attribute('data-scene'))
+        return json.loads(gzip.decompress(self.page.request.get(url).body()))
+
+    def read_clipboard(self):
+        if self.browser.browser_type.name != 'webkit':
+            return self.page.evaluate('navigator.clipboard.readText()')
+        # WebKit denies script reads here; verify the real clipboard with a native paste.
+        active = self.page.evaluate_handle('document.activeElement').as_element()
+        editor = self.page.evaluate_handle('''() => {
+            const editor = document.createElement('textarea');
+            editor.style = 'position:fixed;top:0;left:0;z-index:99999';
+            document.body.append(editor); editor.focus(); return editor;
+        }''').as_element()
+        try:
+            self.page.keyboard.press('Meta+V' if sys.platform == 'darwin' else 'Control+V')
+            self.page.wait_for_function('node => node.value.length > 0', arg=editor, timeout=1000)
+            return editor.input_value()
+        finally:
+            editor.evaluate('node => node.remove()')
+            if active and active.evaluate('node => node.isConnected'):
+                active.focus()
+
+    def assert_accessible(self, state):
+        source = Path(__file__).resolve().parents[1] / 'node_modules/axe-core/axe.min.js'
+        self.page.evaluate(source.read_text())
+        report = self.page.evaluate('''async () => {
+            const result = await axe.run(document);
+            const summarize = (rules) => rules.map(rule => ({id: rule.id, impact: rule.impact,
+                help_url: rule.helpUrl, nodes: rule.nodes.map(node => ({target: node.target, reason: node.failureSummary}))}));
+            return {engine: result.testEngine, environment: result.testEnvironment,
+                violations: summarize(result.violations), needs_review: summarize(result.incomplete)};
+        }''')
+        self.assertEqual(report['engine']['version'], '4.14.0')
+        print('Accessibility:', json.dumps({'state': state, **report}), flush=True)
+        blocking = [rule for rule in report['violations']
+                    if rule['impact'] in ['serious', 'critical'] or rule['id'] in
+                    ['aria-allowed-role', 'heading-order', 'landmark-no-duplicate-banner', 'landmark-unique']]
+        self.assertEqual(blocking, [], json.dumps(blocking, indent=2))
+
+    def test_accessibility_atlas(self):
+        self.visit('atlas')
+        expect(self.page.locator('.atlas-row').first).to_be_visible()
+        self.assert_accessible('atlas')
+
+    def test_accessibility_atlas_details(self):
+        self.visit('problem/MaximumIndependentSet')
+        expect(self.page.locator('.typst-detail')).to_contain_text('wireless network scheduling')
+        with self.subTest('named problem tools'):
+            expect(self.page.get_by_role('group', name='Problem tools', exact=True)).to_be_visible(timeout=500)
+        with self.subTest('article follows the page heading'):
+            expect(self.page.get_by_role('heading', name='Definition', level=2, exact=True)).to_be_visible(timeout=500)
+        self.assert_accessible('atlas-details')
+
+    def test_problem_code_block_is_reachable_and_scrolls_with_keyboard(self):
+        self.visit('problem/MaximumIndependentSet')
+        expect(self.page.locator('.typst-detail')).to_contain_text('wireless network scheduling')
+        code = self.page.locator('.typst-detail pre').first
+        self.page.locator('#main').focus()
+        for _ in range(40):
+            self.page.keyboard.press('Tab')
+            if code.evaluate('(node) => node === document.activeElement'):
+                break
+        else:
+            self.fail('Scrollable code could not be reached with Tab')
+        self.page.evaluate('() => document.fonts.ready')
+        self.assertGreater(code.evaluate('(node) => node.scrollHeight - node.clientHeight'), 0)
+        before = code.evaluate('(node) => node.scrollTop')
+        self.page.keyboard.press('ArrowUp' if before > 0 else 'ArrowDown', delay=100)
+        self.page.wait_for_function('({node, before}) => node.scrollTop !== before',
+                                    arg={'node': code.element_handle(), 'before': before}, timeout=500)
+
+    def test_accessibility_atlas_empty(self):
+        self.visit('atlas')
+        self.page.locator('#atlas-search').fill('NoSuchRegisteredProblem')
+        expect(self.page.locator('.empty-state')).to_be_visible()
+        self.assert_accessible('atlas-empty')
+
+    def test_accessibility_graph(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.assert_accessible('graph')
+
+    def test_accessibility_graph_empty_suggestions(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.page.locator('#source').fill('NoSuchRegisteredProblem')
+        expect(self.page.locator('#suggest')).to_contain_text('No matching problem')
+        self.assert_accessible('graph-empty-suggestions')
+
+    def test_accessibility_graph_popover(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.page.locator('.scene-node[data-node="Satisfiability"]').focus()
+        self.page.keyboard.press('Enter')
+        self.assert_accessible('graph-popover')
+
+    def test_accessibility_graph_desktop_drawer(self):
+        self.page.goto(self.base + 'graph.html')
+        self.page.locator('.steps button').first.click()
+        expect(self.page.locator('#drawer-body article')).to_contain_text('Definition')
+        expect(self.page.get_by_role('banner')).to_have_count(1, timeout=500)
+        self.assert_accessible('graph-desktop-drawer')
+
+    def test_accessibility_graph_mobile_drawer(self):
+        self.page.set_viewport_size({'width': 390, 'height': 844})
+        self.page.goto(self.base + 'graph.html')
+        self.page.locator('.steps button').first.click()
+        expect(self.page.locator('#drawer-body article')).to_contain_text('Definition')
+        self.assert_accessible('graph-mobile-drawer')
+
+    def test_graph_combobox_clears_active_option_on_close_and_empty_results(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        source = self.page.locator('#source')
+        source.fill('MIS')
+        expect(source).to_have_attribute('aria-activedescendant', 'opt-0')
+        source.press('Escape')
+        self.assertIsNone(source.get_attribute('aria-activedescendant'))
+        source.fill('NoSuchRegisteredProblem')
+        self.assertIsNone(source.get_attribute('aria-activedescendant'))
+        expect(self.page.get_by_role('status')).to_contain_text('No matching problem', timeout=500)
+        expect(self.page.locator('#suggest [role="option"]')).to_have_attribute('aria-disabled', 'true', timeout=500)
+
+    def test_graph_endpoint_variant_repaint_preserves_keyboard_focus(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.choose_endpoint('source', 'MIS')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        weight = self.page.locator('#source-options [aria-label="weight"]').get_by_role('button', name='i64', exact=True)
+        weight.focus()
+        weight.press('Enter')
+        expect(weight).to_have_attribute('aria-pressed', 'true')
+        expect(weight).to_be_focused(timeout=500)
+
+    def test_graph_popover_metadata_has_readable_contrast(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.page.locator('.scene-node[data-node="MaximumIndependentSet"]').focus()
+        self.page.keyboard.press('Enter')
+        expect(self.page.locator('#pop')).to_be_visible()
+        samples = self.page.locator('#pop .opt-key').evaluate_all('''nodes => nodes.map(node => {
+            const canvas = document.createElement('canvas'); canvas.width = canvas.height = 1;
+            const ctx = canvas.getContext('2d');
+            const rgba = color => { ctx.clearRect(0, 0, 1, 1); ctx.fillStyle = color;
+                ctx.fillRect(0, 0, 1, 1); return Array.from(ctx.getImageData(0, 0, 1, 1).data); };
+            return {text: node.textContent, foreground: rgba(getComputedStyle(node).color),
+                background: rgba(getComputedStyle(node.closest('.pop')).backgroundColor)};
+        })''')
+        self.assertGreater(len(samples), 0)
+        def luminance(rgba):
+            self.assertEqual(rgba[3], 255, 'This contrast fixture requires opaque colors')
+            channels = [value / 255 for value in rgba[:3]]
+            linear = [value / 12.92 if value <= 0.04045 else ((value + 0.055) / 1.055) ** 2.4
+                      for value in channels]
+            return sum(weight * value for weight, value in zip([0.2126, 0.7152, 0.0722], linear))
+        for sample in samples:
+            high, low = sorted([luminance(sample['foreground']), luminance(sample['background'])], reverse=True)
+            self.assertGreaterEqual((high + 0.05) / (low + 0.05), 4.5, sample['text'])
+
+    def test_graph_footnotes_have_link_roles_and_restore_reference_focus(self):
+        self.page.goto(self.base + 'graph.html')
+        self.page.locator('.steps button').first.click()
+        reference = self.page.locator('#drawer-body article a[role="doc-noteref"]').first
+        expect(reference).to_be_visible(timeout=500)
+        origin = reference.locator('..').get_attribute('id')
+        target = reference.get_attribute('href')[1:]
+        note = self.page.locator(f'#drawer-body [id="{target}"]')
+        backlink = note.locator(f'a[role="doc-backlink"][href="#{origin}"]')
+        expect(backlink).to_be_visible(timeout=500)
+        reference.click()
+        expect(note).to_be_focused(timeout=500)
+        backlink.click()
+        expect(reference).to_be_focused(timeout=500)
+
     def test_alias_search_and_reset(self):
         self.visit("atlas")
         self.page.locator("#atlas-search").fill("MIS")
@@ -59,30 +245,6 @@ def test_main_navigation_returns_home_from_problem(self):
         expect(home).to_have_attribute('aria-current', 'page')
         expect(self.page.locator('main .hero')).to_be_visible()
 
-    def test_home_navigation_opens_question_board(self):
-        self.visit()
-        tab = self.page.get_by_role('navigation', name='Main navigation').get_by_role('link', name='Open questions', exact=True)
-        tab.click()
-        expect(self.page).to_have_url(self.base + 'open-questions/')
-        expect(self.page.get_by_role('heading', name='Open Question Zoo', exact=True)).to_be_visible()
-        self.page.get_by_role('link', name='All questions', exact=False).click()
-        self.page.get_by_role('searchbox', name='Search the collection').fill('Q001')
-        expect(self.page.locator('.question-item:visible')).to_have_count(1)
-        expect(self.page.locator('.question-item:visible .question-id')).to_have_text('Q001')
-        self.page.locator('.question-item:visible .question-link').click()
-        self.page.get_by_role('link', name='Submit a solution', exact=True).click()
-        expect(self.page.get_by_label('Registry entry', exact=True)).to_have_value('Q001')
-        registry = self.page.request.get(self.base + 'open-questions/registry.json').json()
-        question = next(entry for entry in registry['questions'] if entry['id'] == 'Q001')
-        expect(self.page.get_by_role('link', name='Edit registry entry on GitHub')).to_have_attribute(
-            'href', f"https://github.com/GiggleLiu/autoresearch-gadgets/edit/main/registry/{question['slug']}.json")
-
-    def test_graph_navigation_opens_question_board(self):
-        self.page.goto(self.base + 'graph.html')
-        self.page.get_by_role('link', name='Open questions', exact=True).click()
-        expect(self.page).to_have_url(self.base + 'open-questions/')
-        expect(self.page.get_by_role('heading', name='Open Question Zoo', exact=True)).to_be_visible()
-
     def test_home_formulas_load_as_typeset_vectors(self):
         self.visit()
         for name in ['sat', 'qubo']:
@@ -103,15 +265,26 @@ def test_large_resources_load_only_when_needed(self):
         self.assertFalse(any('atlas-data.' in url or 'graph-details.' in url for url in requests))
         self.page.locator('[data-nav="atlas"]').click()
         expect(self.page.locator('.atlas-row').first).to_be_visible()
-        self.assertEqual(sum('atlas-data.json' in url for url in requests), 1)
+        self.assertFalse(any('atlas-data.' in url or '/problem-data/' in url for url in requests))
+        self.page.locator('#atlas-search').fill('MIS')
+        self.page.locator('.atlas-row').click()
+        expect(self.page.locator('.typst-detail')).to_contain_text('wireless network scheduling')
+        self.assertEqual(sum('/problem-data/MaximumIndependentSet.json' in url for url in requests), 1)
+        self.assertEqual(sum('graph-details.json' in url for url in requests), 1)
+        self.assertTrue(self.page.evaluate('''() => {
+            const resources = performance.getEntriesByType('resource');
+            const index = resources.find(r => r.name.includes('graph-details.json'));
+            const record = resources.find(r => r.name.includes('/problem-data/'));
+            return index.startTime < record.responseEnd;
+        }'''))
         requests.clear()
         self.page.goto(self.base + 'graph.html')
-        expect(self.page.locator('#cy canvas').first).to_be_visible()
+        expect(self.page.locator('#cy svg.graph-scene').first).to_be_visible()
         self.assertFalse(any('layout-bundle' in url or 'graph-details.' in url for url in requests))
-        self.page.locator('#browser-search').fill('Bin Packing')
-        self.page.locator('.browser-item').first.click()
+        self.open_problem_popover('BinPacking')
+        self.page.get_by_role('button', name='Details', exact=True).click()
         expect(self.page.locator('.typst-detail')).to_contain_text('Definition')
-        self.assertEqual(sum('layout-bundle' in url for url in requests), 1)
+        self.assertFalse(any('layout-bundle' in url for url in requests))
         self.assertEqual(sum('graph-details.json' in url for url in requests), 1)
 
     def test_csp_blocks_inline_event_handlers(self):
@@ -151,12 +324,25 @@ def test_details_cache_evicts_old_articles(self):
         self.visit('problem/ILP')
         expect(self.page.locator('.typst-detail')).to_contain_text('Definition')
         urls = self.page.evaluate('''async () => {
-            const keys = Object.keys(GRAPH_DETAILS.entries).filter(key => key.startsWith('problem:') && key !== 'problem:ILP').slice(0, 25);
-            const detail = document.querySelector('#reference-detail');
-            for (const key of [...keys, keys.at(-1), keys[0]]) {
-                await renderDetails(detail, '', '', key, key, () => {});
+            const resource = performance.getEntriesByType('resource').find(entry => entry.name.includes('graph-details.json'));
+            const index = await (await fetch(resource.name)).json();
+            const keys = Object.keys(index.entries).filter(key => /^problem:[^/]+$/.test(key) && key !== 'problem:ILP').slice(0, 25);
+            for (const key of [...keys, 'atlas', keys.at(-1), keys[0]]) {
+                const hash = key === 'atlas' ? '#atlas' : '#problem/' + encodeURIComponent(key.slice(8));
+                const ready = new Promise(resolve => {
+                    const observer = new MutationObserver(() => {
+                        const article = document.querySelector('.typst-detail');
+                        if (key === 'atlas' ? document.querySelector('#atlas-search') :
+                            article?.dataset.contentKey?.split('/')[0] === key && article.textContent.includes('Definition')) {
+                            observer.disconnect(); resolve();
+                        }
+                    });
+                    observer.observe(document.querySelector('main'), {childList:true, subtree:true, attributes:true});
+                });
+                location.hash = hash;
+                await ready;
             }
-            return [keys[0], keys.at(-1)].map(key => new URL(GRAPH_DETAILS.entries[key], location.href).href);
+            return [keys[0], keys.at(-1)].map(key => new URL(index.entries[key], location.href).href);
         }''')
         self.assertEqual(requests.count(urls[0]), 2)
         self.assertEqual(requests.count(urls[1]), 1)
@@ -169,11 +355,8 @@ def test_text_sizes_preserve_reading_hierarchy(self):
                                ('.variant-control select', 15), ('.typst-detail p', 16)]:
             expect(self.page.locator(selector).first).to_have_css('font-size', f'{size}px')
         self.page.goto(self.base + 'graph.html')
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        expect(self.page.locator('.browser-item').first).to_be_visible()
-        for selector, size in [('.browser-item small', 13), ('.graph-legend', 13),
-                               ('.inspector-heading span', 14), ('.browser-item', 15),
-                               ('.graph-detail', 16)]:
+        expect(self.page.locator("#cy svg.graph-scene").first).to_be_visible()
+        for selector, size in [('.brand', 15), ('.end input', 16), ('.path .chain', 14)]:
             expect(self.page.locator(selector).first).to_have_css('font-size', f'{size}px')
 
     def test_search_text_cannot_inject_markup(self):
@@ -216,7 +399,7 @@ def test_reduction_evidence_and_typst_proof(self):
         expect(self.page.locator('main')).not_to_contain_text('Graph preserved; solution complemented')
         source = self.page.locator('.rule-endpoint a').first
         expect(source).to_be_visible()
-        expect(self.page.locator('.rule-endpoint a [aria-hidden="true"]')).to_have_text(['↗', '↗'])
+        expect(self.page.locator('.rule-endpoint a .arrow')).to_have_count(2)
         expect(self.page.locator('h1 a')).to_have_count(0)
         expect(self.page.locator('.rule-endpoints dt')).to_have_text(['Source', 'Target'])
         self.assertTrue(self.page.evaluate('''() =>
@@ -251,7 +434,7 @@ def test_clipboard(self):
         self.visit()
         self.page.get_by_role("button", name="Copy installation command").click()
         expect(self.page.locator(".toast")).to_have_text("Command copied to clipboard")
-        self.assertEqual(self.page.evaluate("navigator.clipboard.readText()"),
+        self.assertEqual(self.read_clipboard(),
                          "cargo install problemreductions-cli")
 
     def test_unknown_record_has_recovery(self):
@@ -267,7 +450,7 @@ def test_implementation_links_follow_main(self):
                             ('reduction/MinimumVertexCover/MaximumIndependentSet', 'src/rules/minimumvertexcover_maximumindependentset.rs'),
                             ('reduction/MaximumIndependentSet/DecisionMaximumIndependentSet', 'src/models/decision.rs')]:
             self.visit(route)
-            expect(self.page.get_by_role('link', name='Open API reference ↗', exact=True)).to_be_visible()
+            expect(self.page.get_by_role('link', name='Open API reference', exact=True)).to_be_visible()
             expect(self.page.get_by_role('link', name='Open implementation')).to_have_attribute(
                 'href', 'https://github.com/CodingThrust/problem-reductions/blob/main/' + path)
 
@@ -291,8 +474,8 @@ def test_research_anchor_and_back_navigation(self):
         self.visit()
         expect(self.page.get_by_role("navigation", name="Main navigation")
                .get_by_role("link", name="Research", exact=True)).to_have_count(0)
-        self.page.get_by_role("link", name="Research loop", exact=False).click()
-        expect(self.page.locator("#research")).to_be_in_viewport()
+        self.page.locator(".hero").get_by_role("link", name="Get started").click()
+        expect(self.page.locator("#infrastructure")).to_be_in_viewport()
         self.page.go_back()
         expect(self.page.locator(".hero")).to_be_in_viewport()
 
@@ -302,21 +485,13 @@ def test_documentation_is_reachable(self):
         self.assertTrue(self.page.url.endswith("/introduction.html"))
         expect(self.page.get_by_role("heading", name="Problem Reductions", exact=True)).to_be_visible()
         self.assertNotIn("{{#include", self.page.locator("body").inner_text())
-        self.page.get_by_role('navigation', name='Documentation resources').get_by_role('link', name='Home ↗', exact=True).click()
+        self.page.get_by_role('navigation', name='Documentation resources').get_by_role('link', name='Home', exact=True).click()
         expect(self.page.locator('main .hero')).to_be_visible()
 
-    def test_legacy_documentation_urls_redirect(self):
+    def test_legacy_reduction_graph_url_redirects(self):
         self.page.goto(self.base + 'reduction-graph.html')
         self.page.wait_for_url(self.base + 'graph.html')
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        self.page.goto(self.base + 'open-problems.html')
-        self.page.wait_for_url(self.base + 'open-questions/')
-        expect(self.page.get_by_role('heading', name='Open Question Zoo', exact=True)).to_be_visible()
-
-    def test_legacy_open_questions_hash_opens_question_board(self):
-        self.visit('open-questions')
-        expect(self.page).to_have_url(self.base + 'open-questions/')
-        expect(self.page.get_by_role('heading', name='Open Question Zoo', exact=True)).to_be_visible()
+        expect(self.page.locator("#cy svg.graph-scene").first).to_be_visible()
 
     def test_docs_sidebar_drag_resizes_content(self):
         self.page.goto(self.base + 'introduction.html')
@@ -331,282 +506,23 @@ def test_docs_sidebar_drag_resizes_content(self):
         self.page.mouse.up()
         self.assertGreater(sidebar.bounding_box()['width'], before + 100)
         self.assertGreater(self.page.locator('.content').bounding_box()['x'], content_before + 100)
+        logo = self.page.locator('.docs-brand img')
+        response = self.page.request.get(urljoin(self.page.url, logo.get_attribute('src')))
+        self.assertEqual(response.status, 200)
+        viewbox = ET.fromstring(response.text()).attrib['viewBox'].split()
+        ratio = float(viewbox[2]) / float(viewbox[3])
         for width in [150, 420]:
             box = handle.bounding_box()
             self.page.mouse.move(box['x'] + box['width'] / 2, 100)
             self.page.mouse.down()
             self.page.mouse.move(width, 100, steps=8)
             self.page.mouse.up()
-            logo = self.page.locator('.docs-brand img')
             bounds = logo.bounding_box()
             self.assertLessEqual(bounds['width'], 204)
             self.assertLessEqual(bounds['x'] + bounds['width'], sidebar.bounding_box()['width'] - 17)
-            ratio = logo.evaluate('img => img.naturalWidth / img.naturalHeight')
             self.assertAlmostEqual(bounds['width'] / bounds['height'], ratio, delta=0.02)
             expect(self.page.locator('.docs-brand')).to_have_css('height', '78px')
 
-    def test_graph_motion_expands_and_cleans_up_after_interruption(self):
-        self.page.emulate_media(reduced_motion="no-preference")
-        self.page.goto(self.base + "graph.html")
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        self.page.locator('#graph-search').fill('MIS')
-        self.page.locator('#graph-search').press('Enter')
-        self.page.wait_for_function("() => document.querySelector('#cy')._cyreg.cy.getElementById('MaximumIndependentSet').children().length > 0")
-        samples = self.page.evaluate("""async () => {
-            const cy = document.querySelector('#cy')._cyreg.cy;
-            const node = cy.getElementById('MaximumIndependentSet').children().first();
-            const first = {...node.position()};
-            await new Promise(resolve => setTimeout(resolve, 400));
-            return [first, {...node.position()}];
-        }""")
-        self.assertNotEqual(samples[0], samples[1], 'Variants should move out from the family')
-        self.page.get_by_role('button', name='Reset view').click()
-        self.page.locator('#graph-search').fill('ILP')
-        self.page.locator('#graph-search').press('Enter')
-        self.page.get_by_role('button', name='Reset view').click()
-        self.page.wait_for_function("""() =>
-            document.querySelector('#cy')._cyreg.cy.nodes('[?isVariant]').length === 0
-        """)
-        expect(self.page.locator('.graph-inspector')).to_be_visible()
-
-    def test_graph_is_in_primary_navigation_and_opens_details(self):
-        self.visit()
-        graph_link = self.page.get_by_role("link", name="Graph", exact=True)
-        expect(graph_link).to_be_visible()
-        graph_link.click()
-        self.assertTrue(self.page.url.endswith("/graph.html"))
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        self.page.locator("#graph-search").fill("MIS")
-        self.page.locator("#graph-search").press("Enter")
-        expect(self.page.locator(".graph-inspector")).to_be_visible()
-        expect(self.page.locator("#selection-type")).to_have_text("Problem")
-        variants = self.page.evaluate("""() => {
-            const cy = document.querySelector('#cy')._cyreg.cy;
-            return cy.getElementById('MaximumIndependentSet').children()
-                .map(node => node.id());
-        }""")
-        self.assertGreater(len(variants), 1)
-        self.assertIn('MaximumIndependentSet/graph=SimpleGraph,weight=i64', variants)
-        self.assertTrue(self.page.evaluate("""() => {
-            const boxes = document.querySelector('#cy')._cyreg.cy.nodes('[?isVariant]')
-                .map(node => node.boundingBox());
-            return boxes.every((a, i) => boxes.slice(i + 1).every(b =>
-                a.x2 <= b.x1 || b.x2 <= a.x1 || a.y2 <= b.y1 || b.y2 <= a.y1));
-        }"""), 'Variant nodes and their labels must not overlap')
-        self.assertTrue(self.page.evaluate("""() => {
-            const cy = document.querySelector('#cy')._cyreg.cy;
-            const children = cy.getElementById('MaximumIndependentSet').children();
-            return children.connectedEdges().some(edge =>
-                edge.source().isChild() && edge.target().isChild());
-        }"""))
-        expect(self.page.locator('#graph-detail > h2')).to_have_text('Maximum Independent Set')
-        self.page.get_by_role("button", name="Reset view").click()
-        expect(self.page.locator(".graph-inspector")).to_be_visible()
-        self.assertEqual(self.page.evaluate("""() =>
-            document.querySelector('#cy')._cyreg.cy
-                .getElementById('MaximumIndependentSet').children().length
-        """), 0)
-        positions = self.page.evaluate("""() =>
-            document.querySelector('#cy')._cyreg.cy.nodes()
-                .map(node => ({id: node.id(), ...node.position()}))
-        """)
-        self.page.locator('#graph-search').fill('ILP')
-        self.page.locator('#graph-search').press('Enter')
-        graph = self.page.request.get(self.base + 'reductions/reduction_graph.json').json()
-        expected_variants = sum(node['name'] == 'ILP' for node in graph['nodes'])
-        self.assertEqual(self.page.evaluate("""expectedVariants => {
-            const cy = document.querySelector('#cy')._cyreg.cy;
-            const parent = cy.getElementById('ILP');
-            const box = parent.boundingBox();
-            const neighbors = parent.children().connectedEdges().connectedNodes()
-                .difference(parent.children());
-            if (parent.children().length !== expectedVariants || neighbors.length <= 50) return ['Missing variants or neighbors'];
-            return neighbors.filter(node => {
-                    const {x, y} = node.position();
-                    return x >= box.x1 && x <= box.x2 && y >= box.y1 && y <= box.y2;
-                }).map(node => node.id());
-        }""", expected_variants), [])
-        displaced = self.page.evaluate("""() =>
-            document.querySelector('#cy')._cyreg.cy.nodes()
-                .filter(node => !node.isParent() && !node.data('isVariant'))
-                .map(node => ({id: node.id(), ...node.position()}))
-        """)
-        original = {node['id']: node for node in positions}
-        moved = [node for node in displaced if node != original[node['id']]]
-        self.assertGreater(len(moved), 0)
-        self.assertLess(len(moved), len(displaced), 'Distant nodes keep their positions')
-        self.page.get_by_role('button', name='Reset view').click()
-        self.assertEqual(self.page.evaluate("""() =>
-            document.querySelector('#cy')._cyreg.cy.nodes()
-                .map(node => ({id: node.id(), ...node.position()}))
-        """), positions)
-
-    def test_graph_details_panel_is_persistent_and_resizable(self):
-        self.page.goto(self.base + "graph.html")
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        panel = self.page.locator('.graph-inspector')
-        expect(panel).to_be_visible()
-        expect(self.page.locator('#graph-detail')).to_be_empty()
-        divider = self.page.get_by_role('separator', name='Resize details panel')
-        expect(divider).to_have_attribute('aria-valuenow', '320')
-        expect(divider).to_have_attribute('aria-valuemin', '240')
-        expect(divider).to_have_attribute('aria-valuemax', re.compile(r'^\d+$'))
-        before = self.page.evaluate("""() => {
-            const cy = document.querySelector('#cy')._cyreg.cy;
-            return {pan: {...cy.pan()}, zoom: cy.zoom(),
-                positions: cy.nodes().map(node => ({id: node.id(), ...node.position()}))};
-        }""")
-        box = divider.bounding_box()
-        self.page.mouse.move(box['x'] + box['width'] / 2, box['y'] + 100)
-        self.page.mouse.down()
-        self.page.mouse.move(box['x'] + box['width'] / 2 - 160, box['y'] + 100)
-        expect(divider).to_have_attribute('aria-valuenow', '480')
-        after = self.page.evaluate("""() => {
-            const cy = document.querySelector('#cy')._cyreg.cy;
-            return {pan: {...cy.pan()}, zoom: cy.zoom(),
-                positions: cy.nodes().map(node => ({id: node.id(), ...node.position()}))};
-        }""")
-        self.assertAlmostEqual(after['pan']['x'], before['pan']['x'] - 80)
-        self.assertAlmostEqual(after['pan']['y'], before['pan']['y'])
-        self.assertEqual(after['zoom'], before['zoom'])
-        self.assertEqual(after['positions'], before['positions'])
-        self.page.mouse.up()
-        divider.press('ArrowRight')
-        expect(divider).to_have_attribute('aria-valuenow', '460')
-        self.page.locator('#graph-search').fill('MIS')
-        self.page.locator('#graph-search').press('Enter')
-        self.page.get_by_role('button', name='Reset view').click()
-        expect(panel).to_be_visible()
-        expect(divider).to_have_attribute('aria-valuenow', '460')
-        divider.press('Home')
-        expect(divider).to_have_attribute('aria-valuenow', '240')
-        divider.press('ArrowRight')
-        expect(divider).to_have_attribute('aria-valuenow', '240')
-        divider.press('End')
-        expect(divider).to_have_attribute('aria-valuenow', divider.get_attribute('aria-valuemax'))
-
-    def test_graph_hint_stays_top_right_when_panel_resizes(self):
-        self.page.goto(self.base + 'graph.html')
-        expect(self.page.locator('#cy canvas').first).to_be_visible()
-        divider = self.page.get_by_role('separator', name='Resize details panel')
-        for key in ['Home', 'End']:
-            divider.press(key)
-            legend = self.page.locator('.graph-legend').bounding_box()
-            note = self.page.locator('.graph-canvas-note').bounding_box()
-            canvas = self.page.locator('.graph-canvas').bounding_box()
-            self.assertLessEqual(note['y'] + note['height'], legend['y'])
-            self.assertAlmostEqual(note['y'] - canvas['y'], 18)
-            self.assertAlmostEqual(canvas['x'] + canvas['width'] - note['x'] - note['width'], 18)
-            for box in [legend, note]:
-                self.assertGreaterEqual(box['x'], canvas['x'])
-                self.assertLessEqual(box['x'] + box['width'], canvas['x'] + canvas['width'])
-
-    def test_graph_local_view_keeps_selection_and_neighbor_labels_readable(self):
-        self.page.goto(self.base + "graph.html")
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        self.page.locator('[data-family="AcyclicPartition"]').click()
-        expect(self.page.locator('#graph-detail > h2')).to_have_text('Acyclic Partition')
-        self.assertTrue(self.page.evaluate("""() => {
-            const cy = document.querySelector('#cy')._cyreg.cy;
-            const selected = cy.getElementById('AcyclicPartition');
-            const nodes = selected.union(selected.neighborhood('node'));
-            return selected.hasClass('selected') && !selected.hasClass('neighbor') &&
-                nodes.every(node => node.visible() && node.style('label') === node.data('label') &&
-                    Number(node.style('text-opacity')) === 1 &&
-                    parseFloat(node.style('font-size')) * cy.zoom() >= 11.9) && cy.zoom() > 1;
-        }"""))
-
-    def test_graph_expanded_problem_keeps_a_compact_neighborhood(self):
-        self.page.goto(self.base + "graph.html")
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        self.page.locator('[data-family="BinPacking"]').click()
-        expect(self.page.locator('#graph-detail > h2')).to_have_text('Bin Packing')
-        self.assertTrue(self.page.evaluate("""() => {
-            const cy = document.querySelector('#cy')._cyreg.cy;
-            const family = cy.getElementById('BinPacking');
-            const variants = family.children();
-            const box = family.renderedBoundingBox();
-            return variants.length === 2 && box.w < 500 && box.h < 350 &&
-                variants.connectedEdges().every(edge => {
-                    const a = edge.source().position(), b = edge.target().position();
-                    return Math.hypot(a.x - b.x, a.y - b.y) < 450;
-                });
-        }"""))
-
-    def test_graph_problem_selection_highlights_and_reveals_list_item(self):
-        self.page.goto(self.base + "graph.html")
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        self.page.evaluate("""() => {
-            document.querySelector('#cy')._cyreg.cy.getElementById('QUBO').emit('tap');
-        }""")
-        selected = self.page.locator('#browser-list [data-family="QUBO"]')
-        expect(selected).to_have_attribute('aria-current', 'true')
-        expect(selected).to_be_in_viewport()
-        expect(selected).to_have_text('QUBO2 variants')
-        self.page.evaluate("""() => {
-            document.querySelector('#cy')._cyreg.cy.getElementById('QUBO').children().first().emit('tap');
-        }""")
-        variant = self.page.locator('#browser-list [data-variant][aria-current="true"]')
-        expect(variant).to_be_in_viewport()
-        expect(selected).to_have_attribute('aria-current', 'false')
-
-    def test_graph_shortcuts_leave_text_fields_alone(self):
-        self.page.goto(self.base + "graph.html")
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        selected = self.page.locator('#browser-list [data-family="QUBO"]')
-        selected.click()
-        expect(selected).to_have_attribute('aria-current', 'true')
-        view = "() => { const cy = document.querySelector('#cy')._cyreg.cy; return {zoom: cy.zoom(), pan: {...cy.pan()}}; }"
-        before = self.page.evaluate(view)
-        browser_search = self.page.locator('#browser-search')
-        graph_search = self.page.locator('#graph-search')
-        browser_search.click()
-        self.page.keyboard.type('a/b')
-        expect(browser_search).to_have_value('a/b')
-        expect(browser_search).to_be_focused()
-        expect(graph_search).to_have_value('')
-        expect(self.page.locator('.browser-empty')).to_be_visible()
-        self.page.keyboard.press('Escape')
-        expect(browser_search).to_have_value('')
-        expect(browser_search).not_to_be_focused()
-        expect(selected).to_have_attribute('aria-current', 'true')
-        graph_search.focus()
-        self.page.keyboard.press('Escape')
-        expect(graph_search).not_to_be_focused()
-        expect(selected).to_have_attribute('aria-current', 'true')
-        expect(self.page.locator('#selection-type')).to_have_text('Problem')
-        self.assertEqual(self.page.evaluate(view), before)
-        self.page.keyboard.press('/')
-        expect(graph_search).to_be_focused()
-        expect(graph_search).to_have_value('')
-        self.page.evaluate('document.activeElement.blur()')
-        self.page.keyboard.press('Escape')
-        expect(self.page.locator('#selection-type')).to_have_text('Details')
-        expect(selected).to_have_attribute('aria-current', 'false')
-
-    def test_graph_list_selection_keeps_keyboard_focus(self):
-        self.page.goto(self.base + "graph.html")
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        family = self.page.locator('#browser-list [data-family="QUBO"]')
-        family.focus()
-        self.page.keyboard.press('Enter')
-        expect(family).to_have_attribute('aria-current', 'true')
-        expect(family).to_be_focused()
-        self.page.keyboard.press('Tab')
-        self.page.keyboard.press('Enter')
-        variant = self.page.locator('#browser-list [data-variant][aria-current="true"]')
-        expect(variant).to_be_focused()
-        family.focus()
-        self.page.keyboard.press('Enter')
-        expect(family).to_have_attribute('aria-expanded', 'false')
-        expect(family).to_be_focused()
-        self.page.evaluate("""() => {
-            document.activeElement.blur();
-            document.querySelector('#cy')._cyreg.cy.getElementById('QUBO').emit('tap');
-        }""")
-        expect(family).to_have_attribute('aria-current', 'true')
-        self.assertEqual(self.page.evaluate('document.activeElement.tagName'), 'BODY')
-
     def test_atlas_ilp_prioritizes_documentation_over_metadata(self):
         self.visit('problem/ILP?variant=bounds=general,coefficient=f64,variable=bool')
         expect(self.page.locator('article.typst-detail')).to_contain_text('Lenstra')
@@ -636,227 +552,674 @@ def test_atlas_ilp_prioritizes_documentation_over_metadata(self):
             document.querySelector('#reference-detail').getBoundingClientRect().bottom'''))
         self.assertFalse(self.page.evaluate('document.documentElement.scrollWidth > innerWidth'))
 
-    def test_graph_atlas_link_preserves_variant_and_documentation(self):
+    def choose_endpoint(self, side, query):
+        self.page.locator('#' + side).fill(query)
+        self.page.locator('#' + side).press('Enter')
+
+    def open_problem_popover(self, name):
+        # Initial path selection moves the camera; wait before positioning the node for a click.
+        self.page.wait_for_function("() => !!document.querySelector('.path') && !document.querySelector('.size.pending')")
+        self.page.get_by_role('button', name='Show whole graph', exact=True).click()
+        self.page.locator(f'[data-node="{name}"] .node-disc').click()
+        expect(self.page.locator('#pop')).to_be_visible()
+
+    def copy_route(self):
+        self.page.locator('.copy').click()
+        return json.loads(self.read_clipboard())
+
+    def observe_path_worker(self):
+        # Observe real worker messages without replacing or delaying the engine.
+        self.page.add_init_script("""(() => {
+            const NativeWorker = window.Worker;
+            window.pathMessages = [];
+            window.pathWorkerStarts = 0;
+            window.pathWorkers = [];
+            window.Worker = class extends NativeWorker {
+                constructor(...args) {
+                    super(...args);
+                    window.pathWorkerStarts++;
+                    window.pathWorkers.push(this);
+                }
+                set onmessage(handler) {
+                    super.onmessage = handler;
+                    if (this.observing) return;
+                    this.observing = true;
+                    // Register after the application's handler, including eagerly started workers.
+                    this.addEventListener('message', e => {
+                        window.pathMessages.push(e.data);
+                        window.onPathMessage?.(e.data);
+                    });
+                }
+                get onmessage() { return super.onmessage; }
+            };
+        })()""")
+
+    def test_graph_brand_returns_home(self):
+        self.visit()
+        self.page.get_by_role('link', name='Graph', exact=True).click()
+        expect(self.page.locator('#cy svg.graph-scene').first).to_be_visible()
+        self.page.get_by_role('link', name='Reduction paths', exact=True).click()
+        expect(self.page.locator('main .hero')).to_be_visible()
+
+    def test_graph_pan_zoom_and_node_drag_preserve_route(self):
         self.page.goto(self.base + 'graph.html')
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        self.page.locator('[data-family="MaximumIndependentSet"]').click()
-        self.page.locator('[data-variant="MaximumIndependentSet/graph=SimpleGraph,weight=i64"]').click()
-        expect(self.page.locator('.typst-detail')).to_contain_text('wireless network scheduling')
-        content = self.page.locator('article.typst-detail').inner_html()
-        self.page.get_by_role('link', name='Open in Atlas').click()
-        expect(self.page.locator('#variant-select')).to_have_value('graph=SimpleGraph,weight=i64')
-        expect(self.page.locator('.page-header > p')).to_have_count(0)
-        expect(self.page.locator('.typst-detail')).to_contain_text('wireless network scheduling')
-        self.assertEqual(self.page.locator('article.typst-detail').inner_html(), content)
-        self.page.locator('.detail-references summary').click()
-        expect(self.page.locator('.detail-references li').first).to_be_visible()
-
-    def test_graph_rule_atlas_link_preserves_exact_endpoints(self):
-        self.page.goto(self.base + 'graph.html')
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        self.page.locator('[data-browse="rules"]').click()
-        rule = self.page.evaluate('''() => REDUCTIONS.edges.findIndex(e =>
-            REDUCTIONS.nodes[e.source].name === 'MaximumIndependentSet' &&
-            REDUCTIONS.nodes[e.target].name === 'MaximumClique')''')
-        self.page.locator(f'[data-rule="{rule}"]').click()
-        expect(self.page.locator('article.typst-detail')).to_contain_text('Proof')
-        content = self.page.locator('article.typst-detail').inner_html()
-        endpoints = self.page.locator('.detail-variant').inner_text()
-        self.page.get_by_role('link', name='Open in Atlas').click()
-        expect(self.page.locator('article.typst-detail')).to_contain_text('Proof')
-        self.assertEqual(self.page.locator('article.typst-detail').inner_html(), content)
-        for endpoint in endpoints.split(' → '):
-            expect(self.page.locator('.rule-endpoints')).to_contain_text(endpoint.replace(', ', ' · '))
+        route = self.copy_route()
+        self.page.get_by_role('button', name='Show whole graph', exact=True).click()
+        node = self.page.locator('[data-node="Satisfiability"] .node-disc')
+        center = lambda: node.evaluate('e => {const r=e.getBoundingClientRect(); return {x:r.x+r.width/2,y:r.y+r.height/2,r:r.width/2}}')
+        before = center()
+        self.page.mouse.move(1300, 930)
+        self.page.mouse.down()
+        self.page.mouse.move(1330, 950, steps=3)
+        self.page.mouse.up()
+        moved = center()
+        self.assertAlmostEqual(moved['x'] - before['x'], 30, delta=1)
+        self.assertAlmostEqual(moved['y'] - before['y'], 20, delta=1)
+        self.page.get_by_role('button', name='Zoom in', exact=True).click()
+        zoomed = center()
+        self.assertAlmostEqual(zoomed['r'] / moved['r'], 1.3, delta=.02)
+        self.page.mouse.move(zoomed['x'], zoomed['y'])
+        self.page.mouse.down()
+        self.page.mouse.move(zoomed['x'] + 50, zoomed['y'] + 40, steps=5)
+        self.page.mouse.up()
+        dragged = center()
+        self.assertAlmostEqual(dragged['x'] - zoomed['x'], 50, delta=1)
+        self.assertAlmostEqual(dragged['y'] - zoomed['y'], 40, delta=1)
+        self.assertEqual(self.copy_route(), route)
 
-    def test_graph_details_load_on_demand_and_reuse_family_content(self):
-        requests = []
-        self.page.on('request', lambda request: requests.append(request.url)
-                     if '/assets/details/' in request.url else None)
-        self.page.goto(self.base + 'graph.html')
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        expect(self.page.locator('[data-family="AcyclicPartition"] small')).to_have_count(0)
-        expect(self.page.locator('[data-family="BinPacking"] small')).to_have_text('2 variants')
-        self.assertEqual(requests, [])
-        self.page.locator('[data-family="MaximumIndependentSet"]').click()
-        expect(self.page.locator('.typst-detail')).to_contain_text('wireless network scheduling')
-        self.assertEqual(len(requests), 1)
-        self.page.locator('[data-variant="MaximumIndependentSet/graph=SimpleGraph,weight=i64"]').click()
-        expect(self.page.locator('.typst-detail')).to_contain_text('wireless network scheduling')
-        self.assertEqual(len(requests), 1)
-        self.page.locator('.detail-references summary').click()
-        expect(self.page.locator('.detail-references li').first).to_be_visible()
-        self.assertEqual(len(requests), 2)
-        self.assertTrue(self.page.locator('.typst-detail').evaluate('''article =>
-            [...article.querySelectorAll('use')].every(use =>
-                document.getElementById((use.getAttribute('href') || use.getAttribute('xlink:href')).slice(1)))'''))
-        self.page.locator('[data-browse="rules"]').click()
-        expect(self.page.locator('#browser-list')).not_to_contain_text('Default variant')
-
-    def test_graph_detail_errors_are_visible_and_retryable(self):
-        self.page.route('**/assets/details/problem/BinPacking.html', lambda route: route.fulfill(status=503))
-        self.page.goto(self.base + 'graph.html')
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        self.page.locator('[data-family="BinPacking"]').click()
-        expect(self.page.locator('.typst-detail[role="alert"]')).to_contain_text('503')
-        self.page.unroute('**/assets/details/problem/BinPacking.html')
-        self.page.locator('[data-variant="BinPacking/weight=i64"]').click()
-        expect(self.page.locator('.typst-detail')).to_contain_text('Definition')
-        expect(self.page.locator('.typst-detail[role="alert"]')).to_have_count(0)
-
-    def test_graph_footnote_errors_keep_the_article(self):
-        self.page.route('**/assets/details/footnotes.html', lambda route: route.fulfill(status=503))
-        self.page.goto(self.base + 'graph.html')
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        self.page.locator('[data-family="QUBO"]').click()
-        expect(self.page.locator('.detail-footnotes[role="alert"]')).to_contain_text('503')
-        expect(self.page.locator('article.typst-detail')).to_contain_text('Definition')
-        expect(self.page.locator('article.typst-detail[role="alert"]')).to_have_count(0)
-        self.page.unroute('**/assets/details/footnotes.html')
-        self.page.locator('[data-variant="QUBO/weight=i64"]').click()
-        expect(self.page.locator('.detail-footnotes li')).to_have_count(1)
-        expect(self.page.locator('.detail-footnotes[role="alert"]')).to_have_count(0)
-        self.page.locator('article.typst-detail [role="doc-noteref"] a').click()
-        expect(self.page.locator('.detail-footnotes li')).to_be_in_viewport()
-
-    def test_graph_data_errors_are_visible(self):
-        self.page.route('**/assets/graph-data.js*', lambda route: route.fulfill(status=503))
-        self.page.goto(self.base + 'graph.html')
-        expect(self.page.locator('.graph-canvas-note')).to_contain_text('Unable to load graph: Cannot load graph data')
-        self.assertEqual(len(self.errors), 1)
-        self.errors.clear()
-
-    def test_graph_details_inherit_typst_content_without_changing_variant(self):
-        self.page.goto(self.base + "graph.html")
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        self.page.locator('[data-family="MaximumIndependentSet"]').click()
-        variant = 'MaximumIndependentSet/graph=SimpleGraph,weight=i64'
-        self.page.locator(f'[data-variant="{variant}"]').click()
-        article = self.page.locator('.typst-detail')
-        expect(article).to_have_attribute('data-content-key', 'problem:MaximumIndependentSet')
-        expect(article).to_contain_text('wireless network scheduling')
-        expect(article.locator('figure > svg')).to_have_count(1)
-        expect(self.page.locator('.detail-variant')).to_have_text('graph: SimpleGraph, weight: i64')
-        expect(self.page.locator(f'[data-variant="{variant}"]')).to_have_attribute('aria-current', 'true')
-        self.assertTrue(article.locator('p').first.locator('.typst-math svg').count() > 0)
-        article.locator('a[role="doc-biblioref"]').first.click()
-        expect(self.page.locator('.detail-references')).to_have_attribute('open', '')
-        self.assertTrue(self.page.locator('.graph-inspector').evaluate(
-            '(panel) => panel.scrollWidth <= panel.clientWidth'))
-
-        # A specialized entry takes precedence over the shared family text.
-        self.page.route('**/weighted-detail.html', lambda route: route.fulfill(
-            content_type='text/html', body='<p>Weighted simple-graph documentation.</p>'))
-        self.page.evaluate("""key => {
-            window.GRAPH_DETAILS.entries['problem:' + key] = './weighted-detail.html';
-            document.querySelector('#cy')._cyreg.cy.getElementById(key).emit('tap');
-        }""", variant)
-        expect(article).to_have_attribute('data-content-key', 'problem:' + variant)
-        expect(article).to_have_text('Weighted simple-graph documentation.')
-
-        self.page.locator('[data-browse="rules"]').click()
-        rule = self.page.evaluate("""() => REDUCTIONS.edges.findIndex(rule =>
-            REDUCTIONS.nodes[rule.source].name === 'MaximumIndependentSet' &&
-            REDUCTIONS.nodes[rule.target].name === 'MaximumClique')""")
-        self.page.locator(f'[data-rule="{rule}"]').click()
-        expect(article).to_have_attribute('data-content-key', 'rule:MaximumIndependentSet->MaximumClique')
-        expect(article).to_contain_text('Solution extraction.')
-        expect(article).to_contain_text('pred reduce mis.json')
-        expect(self.page.locator('.detail-source')).to_have_count(0)
-        self.page.get_by_role('button', name='Reset view').click()
-        expect(self.page.locator('#graph-detail')).to_be_empty()
-
-    def test_graph_rule_selection_highlights_matching_list_items(self):
-        self.page.goto(self.base + "graph.html")
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        expected = self.page.evaluate("""() => {
-            const cy = document.querySelector('#cy')._cyreg.cy;
-            const edge = cy.edges().filter(edge => edge.visible()).last();
-            const matches = REDUCTIONS.edges.flatMap((rule, index) =>
-                REDUCTIONS.nodes[rule.source].name === edge.source().id() &&
-                REDUCTIONS.nodes[rule.target].name === edge.target().id() ? [String(index)] : []);
-            edge.emit('tap');
-            return matches;
-        }""")
-        selected = self.page.locator('#browser-list [data-rule][aria-current="true"]')
-        self.assertEqual(selected.evaluate_all('(items) => items.map(item => item.dataset.rule)'), expected)
-        expect(selected.first).to_be_in_viewport()
-        self.assertNotEqual(selected.first.evaluate('(item) => getComputedStyle(item).backgroundColor'),
-                            self.page.locator('#browser-list [aria-current="false"]').first.evaluate(
-                                '(item) => getComputedStyle(item).backgroundColor'))
-
-    def test_graph_browser_lists_real_problems_variants_and_rules(self):
-        self.page.goto(self.base + "graph.html")
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        expected = self.page.evaluate("""() => ({
-            families: new Set(REDUCTIONS.nodes.map(node => node.name)).size,
-            rules: REDUCTIONS.edges.length,
-            rule: REDUCTIONS.edges.findIndex(rule =>
-                REDUCTIONS.nodes[rule.source].name === 'MaximumIndependentSet' &&
-                REDUCTIONS.nodes[rule.target].name === 'MaximumClique')
-        })""")
-        expect(self.page.locator('#browser-list [data-family]')).to_have_count(expected['families'])
-        self.page.locator('#browser-search').fill('MIS')
-        expect(self.page.locator('#browser-list [data-family="MaximumIndependentSet"]')).to_be_visible()
-        self.page.locator('#browser-list [data-family="MaximumIndependentSet"]').click()
-        expect(self.page.locator('#browser-list [data-variant]')).to_have_count(8)
-        variant = 'MaximumIndependentSet/graph=SimpleGraph,weight=i64'
-        self.page.locator(f'#browser-list [data-variant="{variant}"]').click()
-        expect(self.page.locator(f'#browser-list [data-variant="{variant}"]')).to_have_attribute('aria-current', 'true')
-        viewport = self.page.evaluate("""() => {
-            const cy = document.querySelector('#cy')._cyreg.cy;
-            return {zoom: cy.zoom(), pan: cy.pan()};
-        }""")
-        self.page.locator('[data-browse="rules"]').click()
-        expect(self.page.locator('#browser-list [data-rule]')).to_have_count(expected['rules'])
-        self.assertEqual(self.page.evaluate("""() => {
-            const cy = document.querySelector('#cy')._cyreg.cy;
-            return {zoom: cy.zoom(), pan: cy.pan()};
-        }"""), viewport)
-        self.page.locator(f'[data-rule="{expected["rule"]}"]').click()
-        self.assertTrue(self.page.evaluate("""index => {
-            const rule = REDUCTIONS.edges[index];
-            const key = node => node.name + '/' + Object.entries(node.variant)
-                .sort(([a], [b]) => a.localeCompare(b)).map(([k,v]) => `${k}=${v}`).join(',');
-            const edge = document.querySelector('#cy')._cyreg.cy.edges('.selected');
-            return edge.length === 1 && edge.source().id() === key(REDUCTIONS.nodes[rule.source]) &&
-                edge.target().id() === key(REDUCTIONS.nodes[rule.target]);
-        }""", expected['rule']))
-        same_family_rule = self.page.evaluate("""() => REDUCTIONS.edges.findIndex(rule =>
-            REDUCTIONS.nodes[rule.source].name === 'MaximumIndependentSet' &&
-            REDUCTIONS.nodes[rule.target].name === 'MaximumIndependentSet')""")
-        self.page.locator(f'[data-rule="{same_family_rule}"]').click()
-        self.assertTrue(self.page.evaluate("""() => {
-            const edge = document.querySelector('#cy')._cyreg.cy.edges('.selected');
-            return edge.length === 1 && edge.source().id() !== edge.target().id() &&
-                edge.source().parent().id() === 'MaximumIndependentSet' &&
-                edge.target().parent().id() === 'MaximumIndependentSet';
-        }"""))
-        expect(self.page.locator('.typst-detail')).to_contain_text('Proof')
-        self.page.locator('#browser-search').fill('no-such-reduction')
-        expect(self.page.locator('.browser-empty')).to_be_visible()
+    def test_graph_mobile_navigation_controls_are_visible_and_operable(self):
+        self.context.close()
+        self.context = self.browser.new_context(viewport={'width': 320, 'height': 640},
+                                                has_touch=True, reduced_motion='reduce')
+        self.page = self.context.new_page()
+        self.page.set_default_timeout(3000)
+        self.page.on('pageerror', lambda error: self.errors.append(str(error)))
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        controls = self.page.get_by_role('navigation', name='Graph navigation', exact=True)
+        expect(controls).to_be_visible(timeout=500)
+        panel = self.page.locator('.panel').bounding_box()
+        bounds = controls.bounding_box()
+        self.assertGreaterEqual(bounds['x'], 0)
+        self.assertLessEqual(bounds['x'] + bounds['width'], 320)
+        self.assertLessEqual(bounds['y'] + bounds['height'], panel['y'])
+        world = self.page.locator('svg.graph-scene > g')
+        zoom = lambda: world.evaluate('e=>e.getCTM().a')
+        before = zoom()
+        controls.get_by_role('button', name='Zoom in', exact=True).tap()
+        self.assertAlmostEqual(zoom() / before, 1.3, delta=.02)
+        controls.get_by_role('button', name='Zoom out', exact=True).tap()
+        self.assertAlmostEqual(zoom(), before, delta=.001)
+        controls.get_by_role('button', name='Zoom in', exact=True).tap()
+        panned = world.get_attribute('transform')
+        controls.get_by_role('button', name='Show whole graph', exact=True).tap()
+        self.assertNotEqual(world.get_attribute('transform'), panned)
 
-    def test_graph_overview_is_stable_and_labels_do_not_overlap(self):
-        self.page.goto(self.base + "graph.html")
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        positions = self.page.evaluate("""() =>
-            document.querySelector('#cy')._cyreg.cy.nodes()
-                .map(node => ({id: node.id(), ...node.position()}))
-        """)
-        self.page.reload()
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
-        self.assertEqual(self.page.evaluate("""() =>
-            document.querySelector('#cy')._cyreg.cy.nodes()
-                .map(node => ({id: node.id(), ...node.position()}))
-        """), positions)
-        self.page.wait_for_function("""() =>
-            document.querySelector('#cy')._cyreg.cy.nodes('.named').length > 0
-        """)
+    def test_graph_small_mobile_popover_controls_remain_reachable(self):
+        self.page.set_viewport_size({'width': 320, 'height': 640})
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.page.locator('.scene-node[data-node="MaximumIndependentSet"]').focus()
+        self.page.keyboard.press('Enter')
+        details = self.page.locator('#pop .pop-details')
+        for _ in range(20):
+            if details.evaluate('e=>e===document.activeElement'):
+                break
+            self.page.keyboard.press('Tab')
+        else:
+            self.fail('Popover details cannot be reached from its variant controls')
+        bounds = self.page.locator('#pop').bounding_box()
+        header = self.page.locator('.site-header').bounding_box()
+        panel = self.page.locator('.panel').bounding_box()
+        self.assertGreaterEqual(bounds['y'], header['y'] + header['height'])
+        self.assertLessEqual(bounds['y'] + bounds['height'], panel['y'])
+        expect(details).to_be_in_viewport()
+        details.press('Enter')
+        expect(self.page.locator('#drawer-body article')).to_contain_text('Definition')
+
+    def test_graph_touch_pinch_keeps_center_and_route(self):
+        if self.browser.browser_type.name != 'chromium':
+            self.skipTest('Automated multipoint touch injection requires Chromium CDP')
+        self.page.goto(self.base + 'graph.html')
+        route = self.copy_route()
+        matrix = lambda: self.page.locator('svg.graph-scene > g').evaluate('e => {const m=e.getCTM(); return {z:m.a,x:m.e,y:m.f}}')
+        before = matrix()
+        session = self.context.new_cdp_session(self.page)
+        session.send('Emulation.setTouchEmulationEnabled', {'enabled': True, 'maxTouchPoints': 2})
+        def touch(kind, points):
+            session.send('Input.dispatchTouchEvent', {'type': kind, 'touchPoints': [
+                {'x': x, 'y': y, 'id': i} for i, (x, y) in enumerate(points)]})
+        touch('touchStart', [(700, 400), (900, 400)])
+        touch('touchMove', [(650, 400), (950, 400)])
+        touch('touchEnd', [])
+        after = matrix()
+        self.assertAlmostEqual(after['z']/before['z'], 1.5, delta=.02)
+        self.assertAlmostEqual((800-after['x'])/after['z'], (800-before['x'])/before['z'], delta=1)
+        self.assertAlmostEqual((400-after['y'])/after['z'], (400-before['y'])/before['z'], delta=1)
+        touch('touchStart', [(1000, 800)])
+        touch('touchMove', [(1030, 810)])
+        touch('touchCancel', [])
+        panned = matrix()
+        self.assertAlmostEqual(panned['x']-after['x'], 30, delta=1)
+        self.assertAlmostEqual(panned['y']-after['y'], 10, delta=1)
+        self.assertEqual(self.copy_route(), route)
+
+    def test_graph_animated_frame_fits_route_and_wheel_zoom_keeps_cursor_anchor(self):
+        self.page.emulate_media(reduced_motion='no-preference')
+        self.page.goto(self.base + 'graph.html')
+        self.page.wait_for_function('''() => {
+            const done = performance.getEntriesByName('graph:comparison-rendered').at(-1);
+            const camera = performance.getEntriesByName('graph:camera-settled').at(-1);
+            return done && camera && camera.startTime >= done.startTime;
+        }''')
+        self.assertTrue(self.page.locator('.scene-node.route .node-disc').evaluate_all('''nodes => nodes.every(n => {
+            const r=n.getBoundingClientRect(); return r.left >= 392 && r.right <= innerWidth && r.top >= 85 && r.bottom <= innerHeight;
+        })'''))
+        route = self.copy_route()
+        matrix = lambda: self.page.locator('svg.graph-scene > g').evaluate('e => {const m=e.getCTM(); return {z:m.a,x:m.e,y:m.f}}')
+        before = matrix()
+        self.page.mouse.move(1100, 500)
+        self.page.mouse.wheel(0, 100)
+        self.page.wait_for_function('(z) => document.querySelector("svg.graph-scene > g").getCTM().a < z', arg=before['z'])
+        after = matrix()
+        self.assertAlmostEqual((1100-after['x'])/after['z'], (1100-before['x'])/before['z'], delta=1)
+        self.assertAlmostEqual((500-after['y'])/after['z'], (500-before['y'])/before['z'], delta=1)
+        self.assertEqual(self.copy_route(), route)
+
+    def test_graph_has_site_navigation_above_the_canvas(self):
+        self.page.goto(self.base + 'graph.html')
+        navigation = self.page.get_by_role('navigation', name='Main navigation')
+        expect(navigation.get_by_role('link', name='Graph', exact=True)).to_have_attribute('aria-current', 'page')
+        expect(self.page.get_by_role('link', name='Problem Reductions home')).to_be_visible()
+        self.assertGreaterEqual(self.page.locator('.panel').bounding_box()['y'],
+                                navigation.bounding_box()['y'] + navigation.bounding_box()['height'])
+        navigation.get_by_role('link', name='Atlas', exact=True).click()
+        expect(self.page.locator('#atlas-search')).to_be_visible()
+
+    def test_graph_sat_size_badges_finish_promptly_after_routes_arrive(self):
+        self.observe_path_worker()
+        self.page.goto(self.base + 'graph.html')
+        self.page.wait_for_function("() => pathMessages.some(m => m.phase === 'paths')")
+        self.page.wait_for_function("() => pathMessages.some(m => m.phase === 'comparison')", timeout=3000)
+        expect(self.page.locator('.size.pending')).to_have_count(0)
+        expect(self.page.locator('.path').first.locator('.size')).to_contain_text('n')
+
+    def test_graph_unavailable_parameters_keep_size_badges_unknown(self):
+        self.page.goto(self.base + 'graph.html')
+        self.choose_endpoint('source', 'MVC')
+        self.page.locator('#source-options [aria-label="weight"]').get_by_role('button', name='One', exact=True).click()
+        self.choose_endpoint('target', 'LongestCommonSubsequence')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route', timeout=3000)
+        expect(self.page.locator('.path').first.locator('.size')).to_have_text('?', timeout=500)
+
+    def test_graph_engine_download_starts_before_graph_script_finishes(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('.path').first).to_be_visible()
+        timings = self.page.evaluate('''() => {
+            const resources = performance.getEntriesByType('resource');
+            return {wasm:resources.find(r => r.name.includes('path-selection_bg.wasm'))?.startTime,
+                    graph:resources.find(r => r.name.includes('/graph.js'))?.responseEnd};
+        }''')
+        self.assertIsNotNone(timings['wasm'])
+        self.assertLess(timings['wasm'], timings['graph'])
+
+    def test_graph_worker_starts_before_scene_initialization(self):
+        if self.browser.browser_type.name == 'chromium':
+            session = self.context.new_cdp_session(self.page)
+            session.send('Network.enable')
+            session.send('Network.emulateNetworkConditions', {'offline': False, 'latency': 20,
+                         'downloadThroughput': 600000, 'uploadThroughput': 600000})
+        else:
+            print('Instrumentation: CDP network throttling unsupported; worker ordering runs unthrottled', flush=True)
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('.path').first).to_be_visible()
+        snapshot = self.page.evaluate('performance.getEntriesByName("graph:script")[0].detail')
+        self.assertIsNotNone(snapshot, 'Startup instrumentation must record whether its eager worker exists')
+        self.assertIs(snapshot['eager_worker'], True)
+
+    def test_graph_reuses_idle_engine_and_releases_old_cached_queries(self):
+        self.observe_path_worker()
+        self.page.goto(self.base + 'graph.html')
+        self.page.wait_for_function("() => pathMessages.some(m => m.phase === 'comparison')")
+        self.choose_endpoint('source', 'MIS')
+        self.page.wait_for_function("() => pathMessages.filter(m => m.phase === 'comparison').length === 2")
+        self.assertEqual(self.page.evaluate('pathWorkerStarts'), 1)
+        self.choose_endpoint('target', 'SAT')
+        expect(self.page.locator('#results')).to_contain_text('No reduction path')
+        for name in ['MaximumClique', 'MinimumVertexCover', 'MaximumSetPacking', 'Coloring',
+                     'MinimumDominatingSet', 'HamiltonianCircuit', 'Partition', 'SubsetSum', 'MaximumMatching']:
+            self.choose_endpoint('source', name)
+            expect(self.page.locator('#results')).to_contain_text('No reduction path')
+        # Revisiting the oldest query recomputes after the bounded cache has evicted it.
+        self.choose_endpoint('source', 'SAT')
+        before = len(self.page.evaluate('pathMessages'))
+        self.choose_endpoint('target', 'QUBO')
+        self.page.wait_for_function('(before) => pathMessages.length > before', arg=before)
+        expect(self.page.locator('.path').first).to_be_visible()
+        expect(self.page.locator('.size.pending')).to_have_count(0)
+        self.assertEqual(self.page.evaluate('pathWorkerStarts'), 1)
+
+    def test_graph_path_selection_matches_cli_and_keeps_exact_variants(self):
+        self.observe_path_worker()
+        self.page.goto(self.base + 'graph.html')
+        self.choose_endpoint('source', 'MIS')
+        pred = str(Path(__file__).resolve().parents[1] / 'target/debug/pred')
+        reference = json.loads(subprocess.run(
+            [pred, 'path', 'MIS', 'QUBO', '--compare', '--limit', '20', '--json'],
+            check=True, capture_output=True).stdout)
+        self.page.wait_for_function("() => pathMessages.some(m => m.phase === 'comparison')")
+        messages = self.page.evaluate('pathMessages')
+        actual = next(m['result'] for m in messages if m['phase'] == 'paths'
+                      and m['result']['paths'][0]['path'][0]['from']['name'] == 'MaximumIndependentSet')
+        comparison = next(m['result'] for m in messages if m['phase'] == 'comparison')
+        # The page carries only the route itself; the CLI adds per-step and overall parameter metadata.
+        route_only = lambda r: {'steps': r['steps'], 'path': [{'from': s['from'], 'to': s['to']} for s in r['path']]}
+        self.assertEqual(actual['paths'], [route_only(r) for r in reference['paths']])
+        self.assertEqual(actual['truncated'], reference['truncated'])
+        expected = reference['polynomial_comparison']
+        self.assertEqual(comparison['front'], expected['front'])
+        self.assertEqual(comparison['counts'], expected['counts'])
+        self.assertNotIn('pairs', comparison)
+        for actual_profile, expected_profile in zip(comparison['profiles'], expected['profiles'], strict=True):
+            for name, field in actual_profile['fields'].items():
+                self.assertEqual(field['certificate'], expected_profile['fields'][name]['certificate'])
+                self.assertEqual(field['accuracy'], expected_profile['fields'][name]['accuracy'])
+        slower = self.page.get_by_role('button', name=re.compile('^Show .* slower routes$'))
+        if slower.count():
+            slower.click()
+        nodes = self.scene_data()['nodes']
+        chains = set()
+        expect(self.page.locator('.copy')).to_have_text('Copy route for pred reduce --via')
+        for row in self.page.locator('.path').all():
+            n = int(row.get_attribute('data-path'))
+            route = route_only(reference['paths'][n - 1])
+            points = [route['path'][0]['from']] + [step['to'] for step in route['path']]
+            names = [v['name'] for i, v in enumerate(points) if not i or v['name'] != points[i - 1]['name']]
+            self.assertNotIn(tuple(names), chains)
+            chains.add(tuple(names))
+            row.click()
+            self.assertEqual(self.copy_route(), route)
+            self.assertEqual(set(self.page.locator('.scene-node.route').evaluate_all('(nodes) => nodes.map(n => n.dataset.node)')), set(names))
+            groups = []
+            for point in points:
+                if groups and groups[-1][0] == point['name']:
+                    groups[-1][1].append(point['variant'])
+                else:
+                    groups.append((point['name'], [point['variant']]))
+            expect(self.page.locator('.steps li')).to_have_count(len(groups))
+            for i, (name, variants) in enumerate(groups):
+                group = self.page.locator('.steps li').nth(i)
+                if len([n for n in nodes if n['name'] == name]) > 1:
+                    expected = ['   '.join(f'{k}: {v}' for k, v in variant.items()) for variant in variants]
+                    self.assertEqual(group.locator('.kv').all_text_contents(), expected)
+            expect(self.page.get_by_role('button', name='rule', exact=True)).to_have_count(len(groups) - 1)
+            self.assertEqual(self.page.locator('.path[aria-expanded="true"]').get_attribute('data-path'), str(n))
+        count = len(self.page.evaluate('pathMessages'))
+        self.choose_endpoint('source', 'MIS')
+        expect(self.page.locator('.size.pending')).to_have_count(0)
+        self.assertEqual(len(self.page.evaluate('pathMessages')), count)
+        self.page.get_by_role('button', name='Search more', exact=True).click()
+        expect(self.page.locator('.path').first).to_be_visible()
+
+    def test_graph_path_route_copy_solves_and_unreachable_query_is_explicit(self):
+        import tempfile
+        self.page.goto(self.base + 'graph.html')
+        self.choose_endpoint('source', 'MIS')
+        self.choose_endpoint('target', 'MIS')
+        self.page.locator('#target-options [aria-label="weight"]').get_by_role('button', name='i64', exact=True).click()
+        route = self.copy_route()
+        expect(self.page.locator('.steps li')).to_have_count(1)
+        expect(self.page.locator('.steps .kv')).to_have_count(2)
+        expect(self.page.get_by_role('button', name='rule', exact=True)).to_have_count(0)
+        self.assertEqual(route, {'steps': 1, 'path': [{
+            'from': {'name': 'MaximumIndependentSet', 'variant': {'graph': 'SimpleGraph', 'weight': 'One'}},
+            'to': {'name': 'MaximumIndependentSet', 'variant': {'graph': 'SimpleGraph', 'weight': 'i64'}}}]})
+        pred = str(Path(__file__).resolve().parents[1] / 'target/debug/pred')
+        with tempfile.TemporaryDirectory() as directory:
+            path = Path(directory) / 'route.json'
+            path.write_text(json.dumps(route))
+            instance = subprocess.run([pred, 'create', 'MIS', '--graph', '0-1,1-2,2-3,3-4,4-0', '--json'],
+                                      check=True, capture_output=True).stdout
+            bundle = subprocess.run([pred, 'reduce', '-', '--via', str(path), '--json'],
+                                    input=instance, check=True, capture_output=True).stdout
+            result = json.loads(subprocess.run([pred, 'solve', '-', '--solver', 'brute-force', '--json'],
+                                input=bundle, check=True, capture_output=True).stdout)
+        self.assertEqual(result['evaluation'], 'Max(2)')
+        self.assertEqual(sum(result['solution']), 2)
+        self.assertTrue(all(not (result['solution'][u] and result['solution'][v])
+                            for u, v in [(0, 1), (1, 2), (2, 3), (3, 4), (4, 0)]))
+        self.choose_endpoint('target', 'Factoring')
+        expect(self.page.locator('#results')).to_contain_text('No reduction path connects these two.')
+        expect(self.page.locator('.path')).to_have_count(0)
+
+    def test_graph_rows_arrive_before_comparison_and_keep_user_selection(self):
+        self.observe_path_worker()
+        self.page.add_init_script('''window.onPathMessage = message => {
+            if (message.phase !== 'paths') return;
+            window.pendingAtPaths = document.querySelectorAll('.size.pending').length;
+            const row = document.querySelectorAll('.path')[1];
+            row.click();
+            window.chosenDuringComparison = row.dataset.path;
+        };''')
+        self.page.goto(self.base + 'graph.html')
+        self.page.wait_for_function("() => pathMessages.some(m => m.phase === 'comparison')")
+        self.assertGreater(self.page.evaluate('pendingAtPaths'), 0)
+        self.assertEqual(self.page.evaluate('pathMessages.map(m => m.phase)'), ['paths', 'comparison'])
+        expect(self.page.locator('.size.pending')).to_have_count(0)
+        self.assertEqual(self.page.locator('.path[aria-expanded="true"]').get_attribute('data-path'),
+                         self.page.evaluate('chosenDuringComparison'))
+
+    def test_graph_path_search_can_be_cancelled_without_blocking_the_page(self):
+        self.observe_path_worker()
+        self.page.add_init_script('''window.onPathMessage = message => {
+            if (message.phase !== 'paths') return;
+            window.onPathMessage = null;
+            window.pendingAtCancellation = document.querySelectorAll('.size.pending').length;
+            document.querySelector('#results .summary button').click();
+        };''')
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results')).to_contain_text('Search cancelled.')
+        self.assertGreater(self.page.evaluate('pendingAtCancellation'), 0)
+        self.page.locator('#target').fill('MIS')
+        expect(self.page.locator('#suggest [role="option"]').first).to_contain_text('Maximum Independent Set')
+        self.page.locator('#target').press('Enter')
+        expect(self.page.locator('#target')).to_have_value('Maximum Independent Set')
+
+    def test_graph_drawer_opens_from_popover_for_chosen_variant_and_closes_with_escape(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#details-drawer')).to_be_hidden()
+        self.open_problem_popover('MaximumIndependentSet')
+        self.page.locator('#pop [aria-label="weight"]').get_by_role('button', name='i64', exact=True).click()
+        before = self.page.locator('.scene-node.route').evaluate_all('(nodes) => nodes.map(n => n.dataset.node)')
+        self.page.get_by_role('button', name='Details', exact=True).click()
+        expect(self.page.locator('#details-title')).to_have_text('Maximum Independent Set')
+        expect(self.page.locator('#drawer-body article')).to_contain_text('wireless network scheduling')
+        expect(self.page.locator('#drawer-atlas')).to_have_attribute('href', re.compile('variant=graph%3DSimpleGraph%2Cweight%3Di64'))
+        expect(self.page.locator('.dock')).to_be_hidden()
+        # Opening details keeps the route; the camera may only move so the route stays clear of the drawer.
+        after = self.page.locator('.scene-node.route').evaluate_all('(nodes) => nodes.map(n => n.dataset.node)')
+        self.assertEqual(after, before)
+        self.page.wait_for_timeout(600)
         self.assertTrue(self.page.evaluate("""() => {
-            const labels = document.querySelector('#cy')._cyreg.cy.nodes('.named')
-                .map(node => node.renderedBoundingBox({includeNodes: false, includeLabels: true}));
-            return labels.every((a, i) => labels.slice(i + 1).every(b =>
-                a.x2 <= b.x1 || b.x2 <= a.x1 || a.y2 <= b.y1 || b.y2 <= a.y1));
+            const right = document.querySelector('#details-drawer').getBoundingClientRect().left;
+            return [...document.querySelectorAll('.scene-node.route .node-disc')]
+                .every(n => n.getBoundingClientRect().right <= right);
         }"""))
+        self.page.keyboard.press('Escape')
+        expect(self.page.locator('#details-drawer')).to_be_hidden()
+        expect(self.page.locator('.dock')).to_be_visible()
+
+    def test_graph_drawer_opens_from_step_and_article_problem_links_frame_node(self):
+        self.page.goto(self.base + 'graph.html')
+        route = self.copy_route()
+        self.page.locator('.steps .name').first.click()
+        expect(self.page.locator('#details-title')).to_have_text('Satisfiability')
+        expect(self.page.locator('#drawer-body article')).to_contain_text('Definition')
+        expect(self.page.locator('#drawer-atlas')).to_have_attribute('href', './index.html#problem/Satisfiability')
+        # Most articles have no cross-problem links; this one links to Shortest Common Supersequence.
+        self.page.keyboard.press('Escape')
+        self.open_problem_popover('ShortestCommonSuperstring')
+        self.page.get_by_role('button', name='Details', exact=True).click()
+        expect(self.page.locator('#details-title')).to_have_text('Shortest Common Superstring')
+        expect(self.page.locator('#drawer-body article')).to_contain_text('substring containment')
+        selector = self.page.evaluate("""async () => {
+            const url = performance.getEntriesByType('resource').find(entry => entry.name.includes('graph-details.json')).name;
+            const {anchors} = await (await fetch(url)).json();
+            return [...document.querySelectorAll('#drawer-body article a[href^="#"]')]
+                .find(a => anchors[a.hash.slice(1)] === 'problem:ShortestCommonSupersequence')?.getAttribute('href');
+        }""")
+        self.assertIsNotNone(selector)
+        self.page.locator('#drawer-body article a[href="' + selector + '"]').first.click()
+        expect(self.page.locator('#details-title')).to_have_text('Shortest Common Supersequence')
+        self.assertEqual(self.copy_route(), route)
+
+    def test_graph_drawer_opens_exact_cross_family_rule_from_connector_and_canvas(self):
+        self.page.goto(self.base + 'graph.html')
+        route = self.copy_route()
+        rule = next(step for step in route['path'] if step['from']['name'] != step['to']['name'])
+        self.page.get_by_role('button', name='rule', exact=True).first.click()
+        expect(self.page.locator('#drawer-body article')).to_contain_text('Proof')
+        href = self.page.locator('#drawer-atlas').get_attribute('href')
+        from urllib.parse import parse_qs, urlparse
+        query = parse_qs(urlparse(href).fragment.partition('?')[2], keep_blank_values=True)
+        for side, key in [('from', 'from'), ('to', 'to')]:
+            self.assertEqual(query[key], [','.join(f'{k}={v}' for k, v in sorted(rule[side]['variant'].items()))])
+        title = self.page.locator('#details-title').inner_text()
+        self.page.get_by_role('button', name='Close details', exact=True).click()
+        edge = self.page.locator('[data-edge="' + rule['from']['name'] + '→' + rule['to']['name'] + '"]')
+        point = edge.evaluate("""e => { const p = new DOMPoint((+e.getAttribute('x1') + +e.getAttribute('x2'))/2,
+            (+e.getAttribute('y1') + +e.getAttribute('y2'))/2).matrixTransform(e.getScreenCTM()); return {x:p.x,y:p.y}; }""")
+        self.page.mouse.click(point['x'], point['y'])
+        expect(self.page.locator('#details-drawer')).to_be_visible()
+        expect(self.page.locator('#details-title')).to_have_text(title)
+        expect(self.page.locator('#drawer-atlas')).to_have_attribute('href', href)
+        self.assertEqual(self.copy_route(), route)
+
+    def test_graph_details_load_lazily_reuse_family_article_and_preserve_atlas_variant(self):
+        requests = []
+        self.page.on('request', lambda request: requests.append(request.url))
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('.path').first).to_be_visible()
+        self.assertFalse(any('graph-details' in url or '/assets/details/' in url for url in requests))
+        self.open_problem_popover('MaximumIndependentSet')
+        self.page.get_by_role('button', name='Details', exact=True).click()
+        expect(self.page.locator('#drawer-body article')).to_contain_text('wireless network scheduling')
+        self.assertEqual(sum('graph-details.json' in url for url in requests), 1)
+        self.page.keyboard.press('Escape')
+        self.open_problem_popover('MaximumIndependentSet')
+        self.page.locator('#pop [aria-label="weight"]').get_by_role('button', name='i64', exact=True).click()
+        self.page.get_by_role('button', name='Details', exact=True).click()
+        expect(self.page.locator('#drawer-body article')).to_have_attribute('data-content-key', 'problem:MaximumIndependentSet')
+        self.assertEqual(sum('/details/problem/MaximumIndependentSet.html' in url for url in requests), 1)
+        read_content = '''node => ({text: node.textContent,
+            formulas: [...node.querySelectorAll('svg, math')].map(item => item.outerHTML),
+            links: [...node.querySelectorAll('a')].map(link => ({text: link.textContent,
+                href: link.getAttribute('href'), role: link.getAttribute('role')}))})'''
+        content = self.page.locator('#drawer-body article').evaluate(read_content)
+        expect(self.page.get_by_role('heading', name='Definition', level=3, exact=True)).to_be_visible()
+        self.page.get_by_role('link', name='Open in Atlas').click()
+        expect(self.page.locator('#variant-select')).to_have_value('graph=SimpleGraph,weight=i64')
+        expect(self.page.locator('article.typst-detail')).to_contain_text('wireless network scheduling')
+        self.assertEqual(self.page.locator('article.typst-detail').evaluate(read_content), content)
+        expect(self.page.get_by_role('heading', name='Definition', level=2, exact=True)).to_be_visible()
+
+    def test_graph_node_names_track_route_and_endpoint_state(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        sat = self.page.locator('.scene-node[data-node="Satisfiability"]')
+        expect(sat).to_have_attribute('aria-label', re.compile('start of the route'), timeout=500)
+        self.choose_endpoint('source', 'MIS')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        expect(self.page.locator('.scene-node[data-node="MaximumIndependentSet"]')).to_have_attribute(
+            'aria-label', re.compile('start of the route'), timeout=500)
+        expect(sat).not_to_have_attribute('aria-label', re.compile('start of the route'), timeout=500)
+
+    def test_graph_click_activation_without_pointer_events_opens_controls(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.page.locator('.scene-node[data-node="Satisfiability"]').dispatch_event('click', {'detail': 0})
+        expect(self.page.locator('#pop .b-start')).to_be_focused(timeout=500)
+        expect(self.page.get_by_role('dialog', name='Satisfiability', exact=True)).to_be_visible(timeout=500)
+
+    def test_graph_space_activation_waits_for_key_release(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.page.locator('.scene-node[data-node="Satisfiability"]').focus()
+        self.page.keyboard.down('Space')
+        expect(self.page.locator('#pop')).to_be_hidden(timeout=500)
+        self.page.keyboard.up('Space')
+        expect(self.page.locator('#pop .b-start')).to_be_focused(timeout=500)
+
+    def test_graph_keyboard_visits_disconnected_families_and_both_ends(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        graph = self.scene_data()
+        names = list(dict.fromkeys(node['name'] for node in graph['nodes']))
+        linked = {graph['nodes'][edge[side]]['name'] for edge in graph['edges'] for side in ['source', 'target']
+                  if graph['nodes'][edge['source']]['name'] != graph['nodes'][edge['target']]['name']}
+        isolated = next((name for name in names[1:-1] if name not in linked), None)
+        self.assertIsNotNone(isolated, 'The registry must retain an isolated-family navigation fixture')
+        node = self.page.locator(f'.scene-node[data-node="{isolated}"]')
+        node.focus()
+        node.press('PageDown')
+        expect(self.page.locator(f'.scene-node[data-node="{names[names.index(isolated) + 1]}"]')).to_be_focused(timeout=500)
+        self.page.keyboard.press('PageUp')
+        expect(node).to_be_focused(timeout=500)
+        self.page.keyboard.press('Home')
+        expect(self.page.locator(f'.scene-node[data-node="{names[0]}"]')).to_be_focused(timeout=500)
+        self.page.keyboard.press('End')
+        expect(self.page.locator(f'.scene-node[data-node="{names[-1]}"]')).to_be_focused(timeout=500)
+
+    def test_graph_keyboard_focus_reveals_a_node_hidden_by_the_search_panel(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.page.get_by_role('button', name='Show whole graph', exact=True).click()
+        node = self.page.locator('.scene-node[data-node="BinPacking"]')
+        dot = node.locator('.node-disc')
+        before = dot.bounding_box()
+        self.page.mouse.move(1300, 930)
+        self.page.mouse.down()
+        self.page.mouse.move(1300 + 200 - before['x'] - before['width'] / 2, 930, steps=2)
+        self.page.mouse.up()
+        panel = self.page.locator('.panel').bounding_box()
+        self.assertLess(dot.bounding_box()['x'], panel['x'] + panel['width'])
+        node.focus()
+        self.assertGreaterEqual(dot.bounding_box()['x'], panel['x'] + panel['width'] + 12)
+        expect(node.locator('.node-label')).to_be_visible(timeout=500)
+        expect(node).to_have_css('opacity', '1', timeout=500)
+
+    def test_graph_keyboard_variant_selection_keeps_focus_in_the_same_group(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        node = self.page.locator('.scene-node[data-node="MaximumIndependentSet"]')
+        node.focus()
+        node.press('Enter')
+        weight = self.page.locator('#pop [aria-label="weight"]').get_by_role('button', name='i64', exact=True)
+        weight.focus()
+        weight.press('Enter')
+        expect(weight).to_have_attribute('aria-pressed', 'true')
+        expect(weight).to_be_focused(timeout=500)
+        self.page.keyboard.press('Escape')
+        expect(node).to_be_focused(timeout=500)
+
+    def test_graph_keyboard_popover_enters_controls_and_returns_to_node(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        node = self.page.locator('.scene-node[data-node="Satisfiability"]')
+        node.focus()
+        node.press('Enter')
+        expect(self.page.locator('#pop .b-start')).to_be_focused(timeout=500)
+        expect(self.page.get_by_role('dialog', name='Satisfiability', exact=True)).to_be_visible(timeout=500)
+        self.page.keyboard.press('Escape')
+        expect(self.page.locator('#pop')).to_be_hidden()
+        expect(node).to_be_focused(timeout=500)
+
+    def test_graph_details_from_keyboard_popover_returns_to_visible_node(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        node = self.page.locator('.scene-node[data-node="Satisfiability"]')
+        node.focus()
+        node.press('Enter')
+        self.page.locator('#pop .pop-details').focus()
+        self.page.keyboard.press('Enter')
+        expect(self.page.locator('#close-details')).to_be_focused(timeout=500)
+        self.page.keyboard.press('Escape')
+        expect(self.page.locator('#details-drawer')).to_be_hidden()
+        expect(node).to_be_focused(timeout=500)
+
+    def test_graph_comparison_completion_preserves_existing_node_focus(self):
+        self.observe_path_worker()
+        self.page.add_init_script("""window.onPathMessage = (message) => {
+            if (message.phase === 'paths')
+                document.querySelector('.scene-node[data-node="Satisfiability"]').focus();
+        };""")
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        expect(self.page.locator('.scene-node[data-node="Satisfiability"]')).to_be_focused(timeout=500)
+
+    def test_graph_startup_camera_keeps_a_focused_isolated_node_visible(self):
+        self.page.emulate_media(reduced_motion='no-preference')
+        self.observe_path_worker()
+        self.page.add_init_script('''window.onPathMessage = message => {
+            if (message.phase === 'paths')
+                document.querySelector('.scene-node[data-node="BinPacking"]').focus();
+        };''')
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        expect(self.page.locator('.scene-node[data-node="BinPacking"]')).to_be_focused(timeout=500)
+        obscured = self.page.evaluate('''async () => {
+            const node = document.querySelector('.scene-node[data-node="BinPacking"]');
+            const end = performance.now() + 600, outside = [];
+            do {
+                const r = node.getBoundingClientRect(), panel = document.querySelector('.panel').getBoundingClientRect();
+                const top = document.querySelector('.site-header').getBoundingClientRect().bottom;
+                if (r.left < panel.right || r.right > innerWidth || r.top < top || r.bottom > innerHeight)
+                    outside.push({left: r.left, right: r.right, top: r.top, bottom: r.bottom});
+                await new Promise(requestAnimationFrame);
+            } while (performance.now() < end);
+            return outside;
+        }''')
+        self.assertEqual(obscured, [], 'Automatic route framing obscured the focused problem')
+
+    def test_graph_mobile_drawer_isolates_background_and_restores_focus(self):
+        self.page.set_viewport_size({'width': 390, 'height': 844})
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        opener = self.page.locator('.steps button').first
+        opener.focus()
+        opener.press('Enter')
+        expect(self.page.locator('#details-drawer')).to_have_attribute('aria-modal', 'true', timeout=500)
+        close = self.page.get_by_role('button', name='Close details', exact=True)
+        expect(close).to_be_focused(timeout=500)
+        self.page.locator('#source').evaluate('(input) => input.focus()')
+        expect(close).to_be_focused(timeout=500)
+        for _ in range(40):
+            self.page.keyboard.press('Tab')
+            self.assertTrue(self.page.evaluate("document.activeElement.closest('#details-drawer') !== null"))
+            if close.evaluate('(button) => button === document.activeElement'):
+                break
+        else:
+            self.fail('Tab did not cycle back to the close control')
+        self.page.keyboard.press('Escape')
+        expect(self.page.locator('#details-drawer')).to_be_hidden()
+        expect(opener).to_be_focused(timeout=500)
+        self.page.locator('#source').focus()
+        expect(self.page.locator('#source')).to_be_focused(timeout=500)
+
+    def test_graph_drawer_changes_modal_behavior_when_resized(self):
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.page.locator('.steps .name').first.click()
+        self.assertIsNone(self.page.locator('#details-drawer').get_attribute('aria-modal'))
+        self.page.locator('#source').focus()
+        expect(self.page.locator('#source')).to_be_focused(timeout=500)
+        for width in [1167, 768, 390]:
+            self.page.set_viewport_size({'width': width, 'height': 844})
+            expect(self.page.locator('#details-drawer')).to_have_attribute('aria-modal', 'true', timeout=500)
+            expect(self.page.locator('#close-details')).to_be_focused(timeout=500)
+            self.assertEqual(self.page.locator('#details-drawer').bounding_box(),
+                             {'x': 0, 'y': 0, 'width': width, 'height': 844})
+            self.page.locator('#source').evaluate('(input) => input.focus()')
+            expect(self.page.locator('#close-details')).to_be_focused(timeout=500)
+        self.page.set_viewport_size({'width': 1168, 'height': 844})
+        expect(self.page.locator('#details-drawer')).not_to_have_attribute('aria-modal', 'true', timeout=500)
+        self.page.locator('#source').focus()
+        expect(self.page.locator('#source')).to_be_focused(timeout=500)
+        self.page.set_viewport_size({'width': 1440, 'height': 1000})
+        expect(self.page.locator('#details-drawer')).not_to_have_attribute('aria-modal', 'true', timeout=500)
+        self.page.locator('#source').focus()
+        expect(self.page.locator('#source')).to_be_focused(timeout=500)
+
+    def test_graph_mobile_drawer_has_no_horizontal_scroll(self):
+        self.page.set_viewport_size({'width':390, 'height':844})
+        self.page.goto(self.base + 'graph.html')
+        self.page.locator('.steps .name').first.click()
+        expect(self.page.locator('#drawer-body article')).to_contain_text('Definition')
+        expect(self.page.get_by_role('button', name='Close details', exact=True)).to_be_visible()
+        self.assertFalse(self.page.evaluate('document.documentElement.scrollWidth > innerWidth'))
+        self.assertEqual(self.page.locator('#details-drawer').bounding_box(), {'x':0, 'y':0, 'width':390, 'height':844})
+        self.page.keyboard.press('Escape')
+        expect(self.page.locator('#details-drawer')).to_be_hidden()
 
 
 def responsive_check(width):
@@ -869,12 +1232,12 @@ def test(self):
                     "document.documentElement.scrollWidth > innerWidth"
                 ), f"Horizontal overflow at {width}px on {route}")
         self.page.goto(self.base + "graph.html")
-        expect(self.page.locator("#cy canvas").first).to_be_visible()
+        expect(self.page.locator("#cy svg.graph-scene").first).to_be_visible()
         self.assertFalse(self.page.evaluate(
             "document.documentElement.scrollWidth > innerWidth"
         ), f"Horizontal overflow at {width}px on graph.html")
-        self.page.locator("#graph-search").fill("MIS")
-        self.page.locator("#graph-search").press("Enter")
+        self.page.locator('.steps .name').first.click()
+        expect(self.page.locator('#details-drawer')).to_be_visible()
         self.assertFalse(self.page.evaluate(
             "document.documentElement.scrollWidth > innerWidth"
         ), f"Horizontal overflow at {width}px with graph details open")
diff --git a/scripts/test_website_build.py b/scripts/test_website_build.py
index 31141f6cc..da7808feb 100644
--- a/scripts/test_website_build.py
+++ b/scripts/test_website_build.py
@@ -2,39 +2,173 @@
 
 from pathlib import Path
 import json
+import itertools
+import math
 import re
 import subprocess
+import shutil
 import tempfile
 import unittest
 
+from playwright.sync_api import expect, sync_playwright
+
 from build_graph_details import SafeDetailHTML
 import build_website
 from finalize_website import finalize
+from check_website import serve_website
 
 ROOT = Path(__file__).resolve().parents[1]
 
 
 class WebsiteBuildTests(unittest.TestCase):
-    def test_question_board_keeps_assets_and_registry_provenance(self):
+    def test_clean_generation_produces_types_and_tracks_schema_changes(self):
+        schemas = subprocess.run([str(ROOT / 'target/debug/examples/export_frontend_schema')],
+                                 capture_output=True, text=True, check=True).stdout
+        json.loads(schemas)
+        with tempfile.TemporaryDirectory() as directory:
+            root = Path(directory) / 'workspace with spaces'
+            (root / 'scripts').mkdir(parents=True)
+            (root / 'docs/website/src/lib').mkdir(parents=True)
+            (root / 'node_modules').symlink_to(ROOT / 'node_modules', target_is_directory=True)
+            for name in ['scripts/generate_website_contracts.mjs',
+                         'docs/website/src/lib/path-worker-data.mts',
+                         *[f'docs/website/{name}.schema.json' for name in
+                           ['atlas-data', 'graph-details', 'graph-scene', 'native-exports', 'path-graph']]]:
+                shutil.copyfile(ROOT / name, root / name)
+            command = ['node', str(root / 'scripts/generate_website_contracts.mjs')]
+            result = subprocess.run(command, input=schemas, capture_output=True, text=True)
+            self.assertEqual(result.returncode, 0, result.stderr)
+            source = root / 'consumer.mts'
+            source.write_text('''
+import type {GraphSceneData} from './docs/website/src/generated/graph-scene.mjs';
+import type {WasmPathResult} from './docs/website/src/generated/wasm-paths.mjs';
+import type {PathRequest, PathReply} from './docs/website/src/lib/path-worker-data.mts';
+export function position(scene: GraphSceneData) { return scene.layout.Alpha.x; }
+const result: WasmPathResult = {paths: [], truncated: false};
+const request: PathRequest = {kind: 'search', source: 0, target: 1, limit: 1};
+const reply: PathReply = {phase: 'paths', result};
+// @ts-expect-error Rust serializes the truncation marker as a boolean.
+result.truncated = 'yes';
+// @ts-expect-error Comparison messages must carry comparison results.
+const wrongReply: PathReply = {phase: 'comparison', result};
+// @ts-expect-error Cached comparison requests require their engine result.
+const wrongRequest: PathRequest = {kind: 'compare', source: 0, target: 1, limit: 1};
+''')
+            typecheck = [str(ROOT / 'node_modules/.bin/tsc'), '--strict', '--noEmit',
+                         '--target', 'ES2022', '--module', 'NodeNext', '--moduleResolution', 'NodeNext',
+                         '--allowImportingTsExtensions', '--skipLibCheck', str(source)]
+            result = subprocess.run(typecheck, cwd=root, capture_output=True, text=True)
+            self.assertEqual(result.returncode, 0, result.stdout + result.stderr)
+            schema_path = root / 'docs/website/graph-scene.schema.json'
+            schema = json.loads(schema_path.read_text())
+            schema['required'].remove('layout')
+            schema_path.write_text(json.dumps(schema))
+            result = subprocess.run(command, input=schemas, capture_output=True, text=True)
+            self.assertEqual(result.returncode, 0, result.stderr)
+            result = subprocess.run(typecheck, cwd=root, capture_output=True, text=True)
+            self.assertNotEqual(result.returncode, 0)
+            self.assertIn("'scene.layout' is possibly 'undefined'", result.stdout)
+
+    def test_frontend_lint_checks_typescript_control_flow(self):
         with tempfile.TemporaryDirectory() as directory:
             root = Path(directory)
-            source = root / 'board'
-            (source / 'assets').mkdir(parents=True)
-            (source / 'assets/site.js').write_text('document.body.dataset.ready = "true";')
-            (source / 'assets/site.css').write_text('body { color: green; }')
-            (source / 'index.html').write_text('<html><head><link rel="stylesheet" href="assets/site.css">'
-                '<script src="assets/site.js" defer></script></head><body>Questions</body></html>')
-            registry = json.dumps({'questions': [{'id': 'Q001', 'solutions': [
-                {'materials': [{'path': 'assets/proof.svg'}]}]}]}) + '\n'
-            (source / 'registry.json').write_text(registry)
-            output = root / 'site/open-questions'
-            build_website.publish_open_questions(source, output)
-            html = (output / 'index.html').read_text()
-            self.assertIn("script-src 'self'", html)
-            for url in re.findall(r'(?:src|href)="([^"]+)"', html):
-                self.assertTrue((output / url.split('?')[0]).is_file(), url)
-            self.assertEqual((output / 'registry.json').read_text(), registry)
-            self.assertEqual((source / 'registry.json').read_text(), registry)
+            source = root / 'docs/website/src/route.ts'
+            source.parent.mkdir(parents=True)
+            config = root / 'eslint.config.mjs'
+            config.write_text(f'export {{default}} from "{(ROOT / "eslint.config.mjs").as_uri()}";\n')
+            source.write_text('export function route(value: number) { switch (value) { '
+                              'case 1: return "first"; case 1: return "second"; default: return "other"; } }')
+            result = subprocess.run([str(ROOT / 'node_modules/.bin/eslint'), str(source), '--format', 'json'],
+                                    cwd=root, capture_output=True, text=True)
+            self.assertEqual(result.returncode, 1, result.stdout + result.stderr)
+            self.assertIn('no-duplicate-case', [message['ruleId'] for report in json.loads(result.stdout)
+                                               for message in report['messages']])
+
+    def test_frontend_build_emits_typescript_for_both_pages(self):
+        with tempfile.TemporaryDirectory() as directory:
+            root = Path(directory)
+            source, output = root / 'source', root / 'output'
+            source.mkdir()
+            style = ':root { --grid: rgba(237, 242, 232, .045); } body { background: #0b110d; } '
+            style += 'output { color: rgb(1, 2, 3); background: '
+            style += 'radial-gradient(ellipse at 62% 48%, transparent 35%, rgba(0,0,0,.4)), '
+            style += 'radial-gradient(circle at 1px 1px, var(--grid) 1px, transparent 0) 0 0 / 24px 24px; '
+            style += 'display: inline-block; width: 40px; height: 40px; }'
+            (source / 'style.css').write_text(style)
+            (source / 'shared.ts').write_text('export function double(value: number) { return value * 2; }\n'
+                                             'document.documentElement.dataset.shared = "loaded";\n')
+            for page, value in [('index', 21), ('graph', 22)]:
+                (source / f'{page}.html').write_text('<!doctype html><html><head><link rel="stylesheet" href="./style.css"></head><body>'
+                    f'<output></output><script type="module" src="./{page}.ts"></script></body></html>')
+                (source / f'{page}.ts').write_text('import { double } from "./shared";\n'
+                    f'const value: number = {value}; '
+                    'document.querySelector("output")!.textContent = String(double(value));')
+            result = subprocess.run(['node', str(ROOT / 'scripts/build_frontend.mjs'), str(source), str(output)],
+                                    capture_output=True, text=True)
+            self.assertEqual(result.returncode, 0, result.stdout + result.stderr)
+            for path in source.glob('*.ts'):
+                path.unlink()
+            finalize(output)
+            with serve_website(output) as base, sync_playwright() as p:
+                browser = p.chromium.launch()
+                try:
+                    page = browser.new_page()
+                    scripts = []
+                    page.on('request', lambda request: scripts.append(request.url.split('?')[0])
+                            if request.url.split('?')[0].endswith('.js') else None)
+                    for name, value in [('index', '42'), ('graph', '44')]:
+                        page.set_content(f'<!doctype html><html><head><style>{style}</style></head><body><output>{value}</output></body></html>')
+                        reference = page.locator('output').screenshot()
+                        scripts.clear()
+                        page.goto(base + name + '.html')
+                        expect(page.locator('output')).to_have_text(value)
+                        expect(page.locator('output')).to_have_css('color', 'rgb(1, 2, 3)')
+                        self.assertEqual(page.locator('output').screenshot(), reference,
+                                         'The build changed rendered CSS pixels')
+                        self.assertEqual(len(scripts), len(set(scripts)), 'A preloaded module was downloaded twice')
+                finally:
+                    browser.close()
+
+    def test_strict_type_checking_rejects_errors_without_emitting_javascript(self):
+        with tempfile.TemporaryDirectory() as directory:
+            root = Path(directory)
+            source = root / 'main.ts'
+            config = root / 'tsconfig.json'
+            config.write_text(json.dumps({'extends': str(ROOT / 'tsconfig.json'), 'include': ['main.ts']}))
+            source.write_text('function double(value: number) { return value * 2; }\ndouble(21);\n')
+            command = [str(ROOT / 'node_modules/.bin/tsc'), '--project', str(config)]
+            result = subprocess.run(command, capture_output=True, text=True)
+            self.assertEqual(result.returncode, 0, result.stdout + result.stderr)
+            source.write_text('function double(value) { return value * 2; }\ndouble(21);\n')
+            result = subprocess.run(command, capture_output=True, text=True)
+            self.assertNotEqual(result.returncode, 0, 'Strict checking accepted an implicit any parameter')
+            self.assertFalse((root / 'main.js').exists(), 'The separate checker emitted runtime code')
+
+    def test_problem_records_preserve_variants_and_incident_endpoints(self):
+        nodes = [{'name': name, 'variant': {'weight': weight}, 'category': 'misc', 'default': weight == 'One',
+                  'parameter_names': [], 'complexity': '1', 'complexity_mathml': build_website.expression_mathml('1'),
+                  'doc_path': f'models/misc/struct.{name}.html', 'api_path': f'models/misc/struct.{name}.html'} for name, weight in
+                 [('Neighbor', 'One'), ('Source', 'One'), ('Target', 'One'), ('Source', 'i64'), ('Remote', 'One'), ('Source', 'f64')]]
+        edges = [{'source': source, 'target': target, 'parameters': [], 'parameter_contract_error': None,
+                  'witness': True, 'aggregate': False, 'turing': False, 'doc_path': 'rules/example/index.html',
+                  'source_path': 'src/rules/example.rs', 'test_path': None, 'api_path': 'rules/trait.ReduceTo.html'}
+                 for source, target in [(1, 2), (3, 0), (0, 4)]]
+        schemas = [{'name': name, 'category': 'misc', 'description': '', 'fields': [],
+                    'module_path': f'problemreductions::models::misc::{name.lower()}',
+                    'source_path': f'src/models/misc/{name.lower()}.rs'} for name in ['Neighbor', 'Source', 'Target', 'Remote']]
+        with tempfile.TemporaryDirectory() as directory:
+            output = Path(directory)
+            build_website.build_problem_records(output, nodes, edges, schemas)
+            record = json.loads((output / 'Source.json').read_text())
+            nodes[0]['category'] = 123
+            with self.assertRaises(subprocess.CalledProcessError):
+                build_website.build_problem_records(output, nodes, edges, schemas)
+        self.assertEqual(record['schemas'], [schemas[1]])
+        self.assertEqual({node['variant']['weight'] for node in record['nodes'] if node['name'] == 'Source'}, {'One', 'i64', 'f64'})
+        self.assertNotIn('Remote', [node['name'] for node in record['nodes']])
+        self.assertEqual([(record['nodes'][edge['source']]['name'], record['nodes'][edge['source']]['variant']['weight'],
+                           record['nodes'][edge['target']]['name']) for edge in record['edges']],
+                         [('Source', 'One', 'Target'), ('Source', 'i64', 'Neighbor')])
 
     def test_documentation_rejects_active_content(self):
         for markup in ['<script>alert(1)</script>', '<img onerror="alert(1)">',
@@ -68,12 +202,24 @@ def test_release_urls_and_csp_cover_inline_scripts(self):
             self.assertIn('releases/', app)
             self.assertFalse((root / 'assets').exists())
 
-    def test_graph_layout_is_reproducible(self):
+    def test_graph_layout_is_reproducible_and_separates_node_circles(self):
         command = ['node', str(ROOT / 'scripts/generate_website_graph_layout.js'),
                    str(ROOT / 'docs/src/reductions/reduction_graph.json')]
         first, second = (subprocess.run(command, check=True, capture_output=True).stdout
                          for _ in range(2))
         self.assertEqual(first, second)
+        positions = json.loads(first)
+        graph = json.loads((ROOT / 'docs/src/reductions/reduction_graph.json').read_text())
+        neighbors = {node['name']: set() for node in graph['nodes']}
+        for edge in graph['edges']:
+            a, b = (graph['nodes'][edge[end]]['name'] for end in ('source', 'target'))
+            if a != b:
+                neighbors[a].add(b)
+                neighbors[b].add(a)
+        radius = lambda name: max(6, min(22, 6 + 2.4 * math.sqrt(len(neighbors[name])))) / 2 + 9
+        for a, b in itertools.combinations(positions, 2):
+            distance = math.hypot(positions[a]['x'] - positions[b]['x'], positions[a]['y'] - positions[b]['y']) * 1.6
+            self.assertGreaterEqual(distance, radius(a) + radius(b) - 0.1, (a, b))
 
 
 if __name__ == '__main__':
diff --git a/scripts/test_website_contracts.mjs b/scripts/test_website_contracts.mjs
new file mode 100644
index 000000000..cb6019fb9
--- /dev/null
+++ b/scripts/test_website_contracts.mjs
@@ -0,0 +1,520 @@
+import { validateNativeExportData, validateWasmPathRequest, validateWasmComparisonRequest, validateGraphSceneData, validateDetailsIndexData, parseWasmPathResult, parseWasmComparison, validateComparisonParameters, validatePathGraphData, validateAtlasSummary, validateAtlasRecord } from './website_contracts.mjs';
+import assert from 'node:assert/strict';
+import { test } from 'node:test';
+import { spawnSync } from 'node:child_process';
+import { mkdtempSync, readFileSync, rmSync, writeFileSync } from 'node:fs';
+import { tmpdir } from 'node:os';
+import { join } from 'node:path';
+import { validatePathRequest, validatePathReply } from '../docs/website/src/lib/path-worker-data.mts';
+
+test('production build rejects JavaScript over the delivery budget', () => {
+  const source = mkdtempSync(join(tmpdir(), 'frontend-budget-'));
+  try {
+    for (const name of ['index', 'graph']) writeFileSync(join(source, `${name}.html`),
+      '<script type="module" src="./large.js"></script>');
+    writeFileSync(join(source, 'large.js'), `document.body.textContent = "${'x'.repeat(350_000)}";`);
+    const result = spawnSync(process.execPath, ['scripts/build_frontend.mjs', source, join(source, 'out')], { encoding: 'utf8' });
+    assert.notEqual(result.status, 0, 'Oversized production JavaScript was accepted');
+    assert.match(result.stderr, /JavaScript size budget/);
+  } finally {
+    rmSync(source, { recursive: true, force: true });
+  }
+});
+
+function scene() {
+  return { nodes: [
+      { name: 'Alpha', category: 'graph', variant: { weight: 'One' }, default: true },
+      { name: 'Alpha', category: 'graph', variant: { weight: 'i64' }, default: false },
+      { name: 'Beta', category: 'misc', variant: {}, default: true },
+    ],
+    edges: [{ source: 1, target: 2, witness: true, turing: false }, { source: 0, target: 2, witness: false, turing: true }],
+    aliases: { Alpha: ['ALPHA'], Beta: [] },
+    layout: { Alpha: { x: -0.5, y: 2 }, Beta: { x: 3.25, y: -1 } },
+  };
+}
+
+test('scene validation preserves variants, edge ordering and fractional layout', () => {
+  const input = scene();
+  assert.deepEqual(validateGraphSceneData(input), input);
+});
+
+test('scene validation rejects malformed shapes and unsafe indices', () => {
+  for (const mutate of [
+    value => { delete value.edges[0].witness; },
+    value => { value.edges[0].turing = null; },
+    value => { value.nodes[0].category = 'unknown'; },
+    value => { value.nodes[0].default = 'true'; },
+    value => { value.layout.Alpha.x = Infinity; },
+    value => { value.edges[0].source = -1; },
+    value => { value.edges[0].source = 0.5; },
+    value => { value.edges[0].source = 9007199254740992; },
+  ]) {
+    const value = scene();
+    mutate(value);
+    assert.throws(() => validateGraphSceneData(value));
+  }
+  for (const value of [null, [], 'scene', 1]) assert.throws(() => validateGraphSceneData(value));
+});
+
+test('scene validation rejects dangling references and ambiguous variants', () => {
+  for (const mutate of [
+    value => { value.edges[0].target = 3; },
+    value => { value.aliases.Missing = ['X']; },
+    value => { delete value.layout.Beta; },
+    value => { value.layout.Missing = { x: 0, y: 0 }; },
+    value => { value.nodes[1].default = true; },
+    value => { value.nodes[2].default = false; },
+    value => { value.nodes[1].variant = { weight: 'One' }; },
+    value => {
+      value.nodes[0].variant = { weight: 'One', graph: 'SimpleGraph' };
+      value.nodes[1].variant = { graph: 'SimpleGraph', weight: 'One' };
+    },
+  ]) {
+    const value = scene();
+    mutate(value);
+    assert.throws(() => validateGraphSceneData(value));
+  }
+});
+
+test('producer validation accepts valid data and fails on an invalid scene', () => {
+  const value = scene();
+  const run = data => spawnSync(process.execPath, ['scripts/validate_website_data.mjs', 'graph-scene'],
+    { input: JSON.stringify(data), encoding: 'utf8' });
+  const valid = run(value);
+  assert.equal(valid.status, 0, valid.stderr);
+  value.edges[0].target = 3;
+  assert.notEqual(run(value).status, 0);
+});
+
+const page = new URL('https://example.test/research/reductions/index.html');
+const articles = new URL('./releases/current/assets/details/', page);
+function details() {
+  return { entries: { 'problem:Alpha': './releases/current/assets/details/problem/Alpha.html',
+      'rule:Alpha->Beta': './releases/current/assets/details/rule/Alpha-%3EBeta.html' },
+    anchors: { 'def:Alpha': 'problem:Alpha' },
+  };
+}
+
+test('documentation index preserves encoded filenames and anchor targets', () => {
+  const value = details();
+  assert.deepEqual(validateDetailsIndexData(value, page, articles), value);
+  const result = spawnSync(process.execPath,
+    ['scripts/validate_website_data.mjs', 'graph-details', page.href, articles.href],
+    { input: JSON.stringify(value), encoding: 'utf8' });
+  assert.equal(result.status, 0, result.stderr);
+});
+
+test('documentation index rejects invalid shapes and dangling anchors', () => {
+  for (const mutate of [
+    value => { value.entries = []; },
+    value => { value.entries = {}; },
+    value => { value.entries.unexpected = './releases/current/assets/details/Alpha.html'; },
+    value => { value.anchors['def:Beta'] = 'problem:Missing'; },
+    value => { value.anchors['def:Alpha'] = null; },
+  ]) {
+    const value = details();
+    mutate(value);
+    assert.throws(() => validateDetailsIndexData(value, page, articles));
+  }
+});
+
+test('documentation index rejects URLs outside the current release article subtree', () => {
+  for (const url of [
+    './index.html', './releases/old/assets/details/Alpha.html',
+    'https://other.test/research/reductions/releases/current/assets/details/Alpha.html',
+    './releases/current/assets/details/../graph.html',
+    './releases/current/assets/details/%2e%2e/graph.html',
+    './releases/current/assets/details/%2e%2e%2fgraph.html',
+    './releases/current/assets/details/%5cAlpha.html',
+    './releases/current/assets/details/%XX.html',
+    './releases/current/assets/details/Alpha.html?release=old',
+    './releases/current/assets/details/Alpha.html#section',
+    './releases/current/assets/details/Alpha.json',
+    'javascript:alert(1)',
+  ]) {
+    const value = details();
+    value.entries['problem:Alpha'] = url;
+    assert.throws(() => validateDetailsIndexData(value, page, articles), url);
+  }
+});
+
+function pathResult() {
+  const source = { name: 'Source', variant: {} };
+  const middle = { name: 'Middle', variant: { graph: 'SimpleGraph', weight: 'One' } };
+  const target = { name: 'Target', variant: { weight: 'i64' } };
+  return { truncated: false, paths: [
+    { steps: 2, path: [{ from: source, to: middle },
+      { from: { name: 'Middle', variant: { weight: 'One', graph: 'SimpleGraph' } }, to: target }] },
+    { steps: 1, path: [{ from: source, to: target }] },
+  ] };
+}
+
+test('WASM path validation preserves route ordering and variant key semantics', () => {
+  const result = pathResult();
+  assert.deepEqual(parseWasmPathResult(JSON.stringify(result)), result);
+  assert.deepEqual(parseWasmPathResult('{"paths":[],"truncated":false}'),
+    { paths: [], truncated: false });
+});
+
+test('WASM path validation rejects invalid shapes and integer domains', () => {
+  for (const mutate of [
+    value => { value.truncated = 'false'; },
+    value => { value.paths[0].steps = 0.5; },
+    value => { value.paths[0].steps = -1; },
+    value => { value.paths[0].steps = 9007199254740992; },
+    value => { value.paths[0].path[0].from.name = ''; },
+    value => { value.paths[0].path[0].from.variant = null; },
+    value => { value.paths[0].path[0].to.variant.weight = 1; },
+    value => { value.paths = Array(1000).fill(value.paths[0]); },
+    value => { value.paths[0].path = []; },
+  ]) {
+    const value = pathResult();
+    mutate(value);
+    assert.throws(() => parseWasmPathResult(JSON.stringify(value)));
+  }
+  for (const text of ['{invalid', 'null', '[]']) assert.throws(() => parseWasmPathResult(text));
+});
+
+test('WASM path validation rejects incorrect step counts and discontinuous variants', () => {
+  for (const mutate of [
+    value => { value.paths[0].steps = 1; },
+    value => { value.paths[0].path[1].from.name = 'Missing'; },
+    value => { value.paths[0].path[1].from.variant.weight = 'i64'; },
+    value => { delete value.paths[0].path[1].from.variant.graph; },
+    value => { value.paths = []; value.truncated = true; },
+  ]) {
+    const value = pathResult();
+    mutate(value);
+    assert.throws(() => parseWasmPathResult(JSON.stringify(value)));
+  }
+});
+
+function pathGraph() {
+  return { nodes: [
+    { name: 'Source', variant: { graph: 'SimpleGraph', weight: 'One' }, default: true, parameter_names: ['m', 'n'] },
+    { name: 'Target', variant: {}, default: true, parameter_names: ['size'] },
+  ], edges: [{ source: 0, target: 1, witness: true, turing: false, parameter_contract_error: null,
+    parameters: [{ field: 'size', contract: 'upper_bound',
+      formula: '9007199254740993 * n^9007199254740993 * 7^-1', reason: null }] }] };
+}
+
+test('path metadata preserves exact formulas, ordering and explicit nulls', () => {
+  const value = pathGraph();
+  assert.deepEqual(validatePathGraphData(value), value);
+  const variants = structuredClone(value);
+  variants.nodes.push({ ...structuredClone(variants.nodes[0]), variant: { weight: 'i64', graph: 'SimpleGraph' }, default: false });
+  variants.edges[0].parameters[0].contract = 'exact';
+  variants.edges[0].turing = true;
+  variants.edges[0].witness = false;
+  assert.deepEqual(validatePathGraphData(variants), variants);
+  const unavailable = structuredClone(value);
+  unavailable.edges[0].parameters[0] = { field: 'size', contract: 'unavailable', formula: null, reason: 'No certified bound' };
+  assert.deepEqual(validatePathGraphData(unavailable), unavailable);
+  const invalidContract = structuredClone(value);
+  invalidContract.edges[0].parameter_contract_error = 'Missing native parameter contract';
+  invalidContract.edges[0].parameters = [];
+  assert.deepEqual(validatePathGraphData(invalidContract), invalidContract);
+  assert.deepEqual(validatePathGraphData({ nodes: value.nodes, edges: [] }),
+    { nodes: value.nodes, edges: [] });
+  const unparameterized = structuredClone(value);
+  unparameterized.nodes[1].parameter_names = [];
+  unparameterized.edges[0].parameters = [];
+  assert.deepEqual(validatePathGraphData(unparameterized), unparameterized);
+});
+
+test('path metadata rejects malformed shapes, flags and unsafe indices', () => {
+  for (const mutate of [
+    value => { value.nodes = []; },
+    value => { value.nodes[0].name = ''; },
+    value => { value.nodes[0].default = 1; },
+    value => { value.nodes[0].variant.weight = 1; },
+    value => { value.nodes[0].parameter_names = ['n', 'n']; },
+    value => { value.edges[0].source = -1; },
+    value => { value.edges[0].source = 0.5; },
+    value => { value.edges[0].target = 9007199254740992; },
+    value => { value.edges[0].witness = 'true'; },
+    value => { value.edges[0].turing = null; },
+    value => { delete value.edges[0].parameter_contract_error; },
+    value => { value.edges[0].parameter_contract_error = ''; },
+  ]) {
+    const value = pathGraph(); mutate(value);
+    assert.throws(() => validatePathGraphData(value));
+  }
+  for (const value of [null, [], 'metadata']) assert.throws(() => validatePathGraphData(value));
+});
+
+test('path metadata rejects ambiguous variants, defaults, edges and target-field references', () => {
+  for (const mutate of [
+    value => { value.nodes.push({ ...value.nodes[0], variant: { weight: 'One', graph: 'SimpleGraph' } }); },
+    value => { value.nodes.push({ ...value.nodes[0], variant: { weight: 'i64' } }); },
+    value => { value.nodes[0].default = false; },
+    value => { value.edges[0].source = 2; },
+    value => { value.edges[0].target = 2; },
+    value => { value.edges.push(structuredClone(value.edges[0])); },
+    value => { value.edges[0].parameters[0].field = 'unknown'; },
+    value => { value.edges[0].parameters.push(structuredClone(value.edges[0].parameters[0])); },
+    value => { value.edges[0].parameters = []; },
+  ]) {
+    const value = pathGraph(); mutate(value);
+    assert.throws(() => validatePathGraphData(value));
+  }
+});
+
+test('path metadata validates parameter tags and nullable formula/reason semantics', () => {
+  for (const mutate of [
+    field => { field.contract = 'guessed'; },
+    field => { field.formula = 9007199254740992; },
+    field => { field.formula = ''; },
+    field => { field.formula = null; },
+    field => { delete field.formula; },
+    field => { field.reason = 'Unexpected reason on a certified formula'; },
+    field => { delete field.reason; },
+    field => { field.contract = 'unavailable'; },
+    field => { field.contract = 'unavailable'; field.formula = null; field.reason = ''; },
+  ]) {
+    const value = pathGraph(); mutate(value.edges[0].parameters[0]);
+    assert.throws(() => validatePathGraphData(value));
+  }
+});
+
+test('the metadata producer accepts a valid graph and rejects a missing target contract', () => {
+  const value = pathGraph();
+  const run = data => spawnSync(process.execPath, ['scripts/validate_website_data.mjs', 'path-graph'],
+    { input: JSON.stringify(data), encoding: 'utf8' });
+  const valid = run(value);
+  assert.equal(valid.status, 0, valid.stderr);
+  value.edges[0].parameters = [];
+  assert.notEqual(run(value).status, 0);
+});
+
+function protocolGraph() {
+  const graph = pathGraph();
+  graph.nodes.push({ name: 'Middle', variant: {}, default: true, parameter_names: ['size'] });
+  graph.edges.push({ ...structuredClone(graph.edges[0]), target: 2 },
+    { ...structuredClone(graph.edges[0]), source: 2, parameters: [{ field: 'size', contract: 'exact', formula: 'size', reason: null }] });
+  return graph;
+}
+function protocolPaths() {
+  const graph = protocolGraph();
+  const endpoint = i => ({ name: graph.nodes[i].name, variant: graph.nodes[i].variant });
+  return { truncated: false, paths: [[0, 1], [0, 2, 1]].map(indices => ({
+    steps: indices.length - 1, path: indices.slice(1).map((to, i) => ({ from: endpoint(indices[i]), to: endpoint(to) })),
+  })) };
+}
+function protocolRequest(cached = false) {
+  return { kind: cached ? 'compare' : 'search', source: 0, target: 1, limit: 2,
+    ...(cached ? { cached: protocolPaths() } : {}) };
+}
+
+test('worker replies consume engine results without a second graph registry', () => {
+  const request = protocolRequest(), paths = protocolPaths();
+  const first = { phase: 'paths', result: paths };
+  assert.deepEqual(validatePathReply(first, request), first);
+  const last = { phase: 'comparison', result: comparison() };
+  assert.deepEqual(validatePathReply(last, request, paths), last);
+  for (const phase of ['paths', 'comparison']) {
+    const error = { phase, error: 'Cannot complete the query' };
+    assert.deepEqual(validatePathReply(error, request, paths), error);
+  }
+  assert.throws(() => validatePathReply(last, request));
+  assert.throws(() => validatePathReply(first, request, paths));
+  assert.throws(() => validatePathReply(first, protocolRequest(true), paths));
+  const empty = { truncated: false, paths: [] };
+  assert.throws(() => validatePathReply(last, request, empty));
+  assert.deepEqual(validatePathReply({ ...first, result: empty }, request), { ...first, result: empty });
+});
+
+test('worker requests preserve search and cached comparison inputs', () => {
+  for (const cached of [false, true]) {
+    const request = protocolRequest(cached);
+    assert.deepEqual(validatePathRequest(request), request);
+  }
+});
+
+test('worker requests reject invalid indices and limits', () => {
+  for (const field of ['source', 'target']) for (const value of [-1, 0.5, NaN, Infinity, 9007199254740992]) {
+    assert.throws(() => validatePathRequest({...protocolRequest(), [field]: value}));
+  }
+  for (const limit of [0, 1000, 1.5, NaN, Infinity]) {
+    assert.throws(() => validatePathRequest({...protocolRequest(), limit}));
+  }
+});
+
+function comparison() {
+  return { counts: { Dominated: 1, Equivalent: 0, Incomparable: 0, Unknown: 0 }, front: [2],
+    profiles: ['n^2', 'n'].map(certificate => ({ source_coordinates: ['m', 'n'],
+      fields: { n: { certificate, accuracy: { kind: 'exact' } } } })),
+  };
+}
+
+test('comparison validation preserves exact strings, profile ordering and summary fields', () => {
+  const value = comparison();
+  value.profiles[0].fields.n.certificate = '9007199254740993 * 7^-1 * n^9007199254740993';
+  assert.deepEqual(parseWasmComparison(JSON.stringify(value), 2), value);
+});
+
+test('comparison results retain source coordinates and target fields from the selected registry variants', () => {
+  const value = comparison();
+  value.profiles[0].source_coordinates = ['n', 'm'];
+  const original = structuredClone(value);
+  validateComparisonParameters(value, ['m', 'n'], ['n']);
+  assert.deepEqual(value, original);
+  for (const mutate of [
+    value => { value.profiles[0].source_coordinates.pop(); },
+    value => { value.profiles[0].source_coordinates.push('unknown'); },
+    value => { delete value.profiles[0].fields.n; },
+    value => { value.profiles[0].fields.other = value.profiles[0].fields.n; },
+  ]) {
+    const invalid = comparison(); mutate(invalid);
+    assert.throws(() => validateComparisonParameters(invalid, ['m', 'n'], ['n']));
+  }
+});
+
+test('comparison validation rejects malformed shapes and unsafe numeric counts', () => {
+  for (const mutate of [
+    value => { value.mode = 'other'; },
+    value => { value.counts.Unknown = 0.5; },
+    value => { value.counts.Unknown = -1; },
+    value => { value.counts.Unknown = 9007199254740992; },
+    value => { value.profiles[0].fields.n.certificate = 1; },
+    value => { delete value.profiles[0].fields.n.certificate; },
+    value => { value.profiles[0].fields.n.accuracy.kind = 'guessed'; },
+    value => { value.profiles[0].source_coordinates = 'n'; },
+    value => { value.profiles[0].fields[''] = value.profiles[0].fields.n; delete value.profiles[0].fields.n; },
+    value => { value.pairs = null; },
+  ]) {
+    const value = comparison();
+    mutate(value);
+    assert.throws(() => parseWasmComparison(JSON.stringify(value), 2));
+  }
+});
+
+test('comparison validation checks profile, coordinate, front and aggregate references', () => {
+  for (const mutate of [
+    value => { value.profiles.pop(); },
+    value => { value.counts.Dominated = 0; },
+    value => { value.front = [0]; },
+    value => { value.front = [3]; },
+    value => { value.front = [2, 2]; },
+    value => { value.front = []; },
+    value => { value.profiles[0].source_coordinates = ['n', 'n']; },
+    value => { value.profiles[0].fields.n.certificate = 'missing'; },
+    value => { value.profiles[0].fields.n.certificate = null; },
+    value => { value.profiles[0].fields.n.accuracy = { kind: 'unavailable', reason: { kind: 'missing_field' } }; },
+    value => { value.pairs = []; },
+  ]) {
+    const value = comparison();
+    mutate(value);
+    assert.throws(() => parseWasmComparison(JSON.stringify(value), 2));
+  }
+});
+
+test('comparison validation accepts nondominated verdicts and all declared unavailable-reason shapes', () => {
+  for (const verdict of ['Equivalent', 'Incomparable', 'Unknown']) {
+    const value = comparison();
+    value.counts = { Dominated: 0, Equivalent: 0, Incomparable: 0, Unknown: 0 };
+    value.counts[verdict] = 1;
+    value.front = [1, 2];
+    value.profiles[0].fields.n.certificate = verdict === 'Incomparable' ? 'm' : 'n';
+    if (verdict === 'Unknown') value.profiles[0].fields.n = {
+      certificate: null, accuracy: { kind: 'unavailable', reason: { kind: 'missing_field' } },
+    };
+    assert.deepEqual(parseWasmComparison(JSON.stringify(value), 2), value);
+  }
+  for (const reason of [{ kind: 'not_polynomial', detail: 'n^-1' }, { kind: 'unavailable', detail: 'No bound' },
+    { kind: 'missing_field' }, { kind: 'validity' }, { kind: 'resource_limit', detail: 'No certificate' }]) {
+    const value = comparison();
+    value.counts = { Dominated: 0, Equivalent: 0, Incomparable: 0, Unknown: 1 };
+    value.front = [1, 2];
+    value.profiles[0].fields.n = { certificate: null, accuracy: { kind: 'unavailable', reason } };
+    assert.deepEqual(parseWasmComparison(JSON.stringify(value), 2), value);
+  }
+});
+
+test('comparison validation covers empty batches and rejects unsafe path counts', () => {
+  const value = { profiles: [], front: [],
+    counts: { Dominated: 0, Equivalent: 0, Incomparable: 0, Unknown: 0 } };
+  assert.deepEqual(parseWasmComparison(JSON.stringify(value), 0), value);
+  for (const count of [-1, NaN, 9007199254740992]) {
+    assert.throws(() => parseWasmComparison(JSON.stringify(comparison()), count));
+  }
+});
+
+function atlasSummary() {
+  return { kind: 'summary',
+    nodes: [{name: 'Alpha', variant: {weight: 'One'}, category: 'graph'}, {name: 'Beta', variant: {}, category: 'misc'}],
+    edges: [{source: 0, target: 1}], schemas: [{name: 'Alpha', description: 'First problem'}, {name: 'Beta', description: 'Second problem'}]};
+}
+function atlasRecord() {
+  const summary = atlasSummary(), mathml = '<math xmlns="http://www.w3.org/1998/Math/MathML" aria-label="n"><mi mathvariant="normal">n</mi></math>';
+  return { kind: 'record',
+    nodes: summary.nodes.map(node => ({...node, default: true, parameter_names: ['n'], complexity: 'n', complexity_mathml: mathml,
+      doc_path: `models/graph/struct.${node.name}.html`, api_path: `models/graph/struct.${node.name}.html`})),
+    edges: [{source: 0, target: 1, witness: true, aggregate: false, turing: false, parameter_contract_error: null,
+      parameters: [{field: 'n', contract: 'exact', formula: '9007199254740993 / 7 * n^9007199254740995', reason: null,
+        mathml: '<math xmlns="http://www.w3.org/1998/Math/MathML" aria-label="9007199254740993 / 7 * n^9007199254740995"><mrow><mfrac><mn>9007199254740993</mn><mn>7</mn></mfrac><mo>·</mo><msup><mi mathvariant="normal">n</mi><mn>9007199254740995</mn></msup></mrow></math>'}],
+      doc_path: 'rules/alpha_beta/index.html', source_path: 'src/rules/alpha_beta.rs', api_path: 'rules/trait.ReduceTo.html', test_path: null}],
+    schemas: [{...summary.schemas[0], category: 'graph', fields: [{name: 'n', type_name: 'u64', description: ''}],
+      module_path: 'problemreductions::models::graph::alpha', source_path: 'src/models/graph/alpha.rs'}]};
+}
+test('Atlas contracts preserve summary metadata, exact formulas and nullable fields', () => {
+  const summary = atlasSummary(), record = atlasRecord();
+  summary.schemas[0].aliases = ['A']; summary.schemas[0].display_name = 'Alpha problem';
+  assert.deepEqual(validateAtlasSummary(structuredClone(summary)), summary);
+  assert.deepEqual(validateAtlasRecord(structuredClone(record), 'Alpha'), record);
+  assert.equal(Object.hasOwn(validateAtlasRecord(record).schemas[0], 'aliases'), false);
+  const producer = spawnSync(process.execPath, ['scripts/validate_website_data.mjs', 'atlas-records'],
+    {input: JSON.stringify([record]), encoding: 'utf8'});
+  assert.equal(producer.status, 0, producer.stderr);
+});
+test('Atlas contracts reject malformed data and unsafe embedded markup or links', () => {
+  for (const mutate of [
+    value => { value.nodes[0].category = 'other'; }, value => { value.edges[0].parameters[0].formula = 9007199254740992; },
+    value => { value.nodes[0].complexity_mathml = '<img src=x onerror=alert(1)>'; },
+    value => { value.edges[0].parameters[0].mathml = '<math><script>alert(1)</script></math>'; },
+    value => { value.nodes[0].api_path = '../index.html'; }, value => { value.schemas[0].aliases = null; },
+  ]) { const record = atlasRecord(); mutate(record); assert.throws(() => validateAtlasRecord(record)); }
+  assert.throws(() => validateAtlasSummary(atlasRecord()));
+  assert.throws(() => validateAtlasRecord(atlasSummary()));
+});
+test('Atlas contracts reject mismatched families and invalid graph references', () => {
+  assert.throws(() => validateAtlasRecord(atlasRecord(), 'Beta'));
+  const summary = atlasSummary(); summary.schemas.pop();
+  assert.throws(() => validateAtlasSummary(summary));
+  const record = atlasRecord(); record.edges[0].target = 2;
+  assert.throws(() => validateAtlasRecord(record));
+  const duplicate = atlasSummary(); duplicate.nodes.push({...duplicate.nodes[0]});
+  assert.throws(() => validateAtlasSummary(duplicate));
+});
+
+function nativeExports() {
+  const record = atlasRecord();
+  return {graph: {
+    nodes: record.nodes.map(({api_path, complexity_mathml, ...node}) => node),
+    edges: record.edges.map(({api_path, source_path, test_path, parameters, ...edge}) =>
+      ({...edge, parameters: parameters.map(({mathml, ...parameter}) => parameter)})),
+    aliases: {Alpha: ['A'], Beta: []}},
+    schemas: record.nodes.map(node => ({name: node.name, category: node.category, description: '',
+      fields: [{name: 'n', type_name: 'u64', description: ''}], module_path: 'problemreductions::models::graph::alpha'}))};
+}
+test('native export boundary preserves exact metadata and rejects malformed registry references', () => {
+  const input = nativeExports();
+  assert.deepEqual(validateNativeExportData(structuredClone(input)), input);
+  for (const mutate of [
+    value => { value.graph.nodes[0].category = 123; }, value => { value.schemas[0].fields = null; },
+    value => { value.graph.edges[0].target = 2; }, value => { value.graph.aliases.Missing = ['X']; },
+    value => { value.schemas[1].name = 'Missing'; },
+  ]) {const value = nativeExports(); mutate(value); assert.throws(() => validateNativeExportData(value));}
+});
+test('Rust-derived request schemas preserve optional fields and reject malformed native input', () => {
+  const query = {graph: protocolGraph(), source: 0, target: 1, limit: 2};
+  assert.equal(validateWasmPathRequest(query), true);
+  const comparison = {graph: query.graph, paths: protocolPaths().paths};
+  assert.equal(validateWasmComparisonRequest(comparison), true);
+  delete query.graph.edges[0].parameter_contract_error;
+  delete query.graph.edges[0].parameters[0].reason;
+  assert.equal(validateWasmPathRequest(query), true);
+  query.graph.nodes[0].parameter_names = [1];
+  assert.equal(validateWasmPathRequest(query), false);
+  assert.equal(validateWasmComparisonRequest({...comparison, paths: [{steps: 1, path: []}]}), false);
+});
diff --git a/scripts/test_website_failures.py b/scripts/test_website_failures.py
new file mode 100644
index 000000000..7d97b65a6
--- /dev/null
+++ b/scripts/test_website_failures.py
@@ -0,0 +1,301 @@
+"""Real HTTP failure/retry checks using mutable copies of the production assets."""
+
+from functools import partial
+import gzip
+import json
+import os
+from pathlib import Path
+import re
+import shutil
+import tempfile
+import time
+from threading import Event, Thread
+import unittest
+
+from playwright.sync_api import expect
+
+from check_website import Handler, PreviewServer
+import test_website
+
+
+class UncachedHandler(Handler):
+    def do_GET(self):
+        if self.path.endswith('/graph-scene.json.gz'):
+            self.server.scene_release.wait(timeout=3)
+        if self.path.endswith('/path-selection_bg.wasm.gz'):
+            self.server.engine_requested.set()
+            self.server.engine_release.wait(timeout=3)
+        super().do_GET()
+
+    def end_headers(self):
+        # Each retry exercises the repaired bytes, rather than a cached bad response.
+        self.send_header('Cache-Control', 'no-store')
+        super().end_headers()
+
+
+class WebsiteFailureTests(test_website.WebsiteTests):
+    @classmethod
+    def setUpClass(cls):
+        source = os.environ.get('WEBSITE_SITE_DIR')
+        if not source:
+            raise unittest.SkipTest('Use check_website.py to supply the production artifact with WEBSITE_SITE_DIR')
+        cls.source = Path(source)
+        super().setUpClass()
+
+    def setUp(self):
+        super().setUp()
+        temporary = tempfile.TemporaryDirectory(prefix='problem-reductions-failure-')
+        self.addCleanup(temporary.cleanup)
+        self.site = Path(temporary.name)
+        for name in ['index.html', 'graph.html']:
+            shutil.copyfile(self.source / name, self.site / name)
+        release = re.search(r'releases/\d+', (self.site / 'graph.html').read_text())[0]
+        shutil.copytree(self.source / release, self.site / release)
+        self.assets = self.site / release / 'assets'
+        server = PreviewServer(('127.0.0.1', 0), partial(UncachedHandler, directory=str(self.site)))
+        self.engine_requested = server.engine_requested = Event()
+        self.engine_release = server.engine_release = Event()
+        self.engine_release.set()
+        self.scene_release = server.scene_release = Event()
+        self.scene_release.set()
+        thread = Thread(target=server.serve_forever, daemon=True)
+        thread.start()
+        self.base = f'http://127.0.0.1:{server.server_port}/'
+        def close():
+            self.engine_release.set()
+            self.scene_release.set()
+            server.shutdown()
+            thread.join()
+            server.server_close()
+        self.addCleanup(close)
+
+    def test_atlas_rejects_invalid_json_and_recovers(self):
+        resource = self.assets / 'problem-data/MaximumIndependentSet.json'
+        original = resource.read_bytes()
+        resource.write_text('{invalid JSON')
+        self.page.goto(self.base + 'index.html#problem/MaximumIndependentSet')
+        expect(self.page.get_by_role('alert')).to_be_visible(timeout=1000)
+        resource.write_bytes(original)
+        self.page.evaluate("location.hash = 'atlas'")
+        self.page.locator('#atlas-search').fill('MIS')
+        self.page.locator('a.atlas-row[href="#problem/MaximumIndependentSet"]').click()
+        expect(self.page.locator('#variant-select')).to_have_value('graph=SimpleGraph,weight=One')
+
+    def assert_engine_recovery(self, name, damaged):
+        resource = self.assets / name
+        original = resource.read_bytes()
+        if damaged is None:
+            resource.unlink()
+        else:
+            resource.write_bytes(damaged)
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results')).to_contain_text('Cannot load the path engine', timeout=1000)
+        expect(self.page.locator('.skeleton, .path')).to_have_count(0)
+        expect(self.page.get_by_role('button', name='Cancel', exact=True)).to_have_count(0)
+        resource.write_bytes(original)
+        self.page.get_by_role('button', name='SAT → QUBO', exact=True).click()
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        route = self.copy_route()
+        self.assertEqual(route['path'][0]['from']['name'], 'Satisfiability')
+        self.assertEqual(route['path'][-1]['to']['name'], 'QUBO')
+
+    def test_graph_recovers_after_missing_worker(self):
+        self.assert_engine_recovery('path-worker.js', None)
+
+    def test_graph_recovers_after_invalid_wasm(self):
+        self.assert_engine_recovery('path-selection_bg.wasm.gz', gzip.compress(b'not a WASM module', mtime=0))
+
+    def test_graph_recovers_after_corrupt_engine_metadata(self):
+        self.assert_engine_recovery('path-graph.json.gz', gzip.compress(b'{invalid JSON', mtime=0))
+
+    def worker_reply(self, request):
+        self.page.goto(self.base + 'index.html')
+        return self.page.evaluate('''({url, request}) => new Promise((resolve, reject) => {
+            const worker = new Worker(url, {type: 'module'});
+            worker.onmessage = event => { worker.terminate(); resolve(event.data); };
+            worker.onerror = event => { worker.terminate(); reject(new Error(event.message)); };
+            worker.postMessage(request);
+        })''', {'url': self.base + self.assets.relative_to(self.site).as_posix() + '/path-worker.js', 'request': request})
+
+    def test_worker_rejects_invalid_request_limit(self):
+        graph = json.loads(gzip.decompress((self.assets / 'path-graph.json.gz').read_bytes()))
+        source = next(i for i, node in enumerate(graph['nodes']) if node['name'] == 'Satisfiability' and node['default'])
+        target = next(i for i, node in enumerate(graph['nodes']) if node['name'] == 'QUBO' and node['default'])
+        reply = self.worker_reply({'kind': 'search', 'source': source, 'target': target, 'limit': 0})
+        self.assertEqual(reply, {'phase': 'paths',
+                                'error': 'Invalid path worker contract. Reload the current release.'})
+
+    def test_worker_rejects_cached_routes_without_witness_capability(self):
+        graph = json.loads(gzip.decompress((self.assets / 'path-graph.json.gz').read_bytes()))
+        edge = next(edge for edge in graph['edges'] if not edge['witness'] or edge['turing'])
+        endpoint = lambda i: {key: graph['nodes'][i][key] for key in ['name', 'variant']}
+        route = {'steps': 1, 'path': [{'from': endpoint(edge['source']), 'to': endpoint(edge['target'])}]}
+        reply = self.worker_reply({'kind': 'compare', 'source': edge['source'], 'target': edge['target'],
+                                   'limit': 1, 'cached': {'truncated': False, 'paths': [route]}})
+        self.assertEqual(reply, {'phase': 'comparison',
+                                'error': 'Path references an unregistered reduction.'})
+
+    def test_graph_rejects_out_of_order_worker_reply_and_recovers(self):
+        self.observe_path_worker()
+        self.engine_release.clear()
+        self.page.goto(self.base + 'graph.html')
+        self.page.wait_for_function('() => pathWorkers[0]?.onmessage && document.querySelector("#results .skeleton")')
+        self.page.evaluate('''() => pathWorkers[0].dispatchEvent(new MessageEvent('message', {
+            data: structuredClone({phase: 'comparison', result: {}})
+        }))''')
+        expect(self.page.locator('#results')).to_contain_text('Cannot load the path engine', timeout=1000)
+        expect(self.page.get_by_role('button', name='Cancel', exact=True)).to_have_count(0)
+        self.engine_release.set()
+        self.page.get_by_role('button', name='SAT → QUBO', exact=True).click()
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.assertEqual(self.copy_route()['path'][-1]['to']['name'], 'QUBO')
+
+    def test_graph_retries_comparison_from_cached_routes_after_native_error(self):
+        self.observe_path_worker()
+        resource = self.assets / 'path-graph.json.gz'
+        original = resource.read_bytes()
+        graph = json.loads(gzip.decompress(original))
+        for edge in graph['edges']:
+            edge['parameter_contract_error'] = 'Native parameter contract is unavailable'
+        resource.write_bytes(gzip.compress(json.dumps(graph).encode(), mtime=0))
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results')).to_contain_text('Cannot load the path engine', timeout=1000)
+        self.assertEqual(self.page.evaluate('pathMessages.map(message => message.phase)'), ['paths', 'comparison'])
+        resource.write_bytes(original)
+        self.page.get_by_role('button', name='SAT → QUBO', exact=True).click()
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.assertEqual(self.page.evaluate('pathMessages.map(message => message.phase)'), ['paths', 'comparison', 'comparison'])
+        self.assertEqual(self.page.evaluate('pathWorkerStarts'), 2)
+        self.assertEqual(self.copy_route()['path'][-1]['to']['name'], 'QUBO')
+
+    def test_graph_growth_preserves_wide_exponents_and_exact_degree_sums(self):
+        resource = self.assets / 'path-graph.json.gz'
+        graph = json.loads(gzip.decompress(resource.read_bytes()))
+        edge = next(edge for edge in graph['edges']
+                    if graph['nodes'][edge['source']]['name'] == 'GraphPartitioning'
+                    and graph['nodes'][edge['source']]['default']
+                    and graph['nodes'][edge['target']]['name'] == 'QUBO'
+                    and graph['nodes'][edge['target']]['default'])
+        formulas = {
+            'num_vars': 'num_vertices^9007199254740993 + num_edges^9007199254740992',
+            'num_quadratic_terms': 'num_edges^9007199254740992 * num_vertices',
+        }
+        for parameter in edge['parameters']:
+            parameter['formula'] = formulas[parameter['field']]
+            parameter['contract'] = 'exact'
+        graph['edges'] = [edge]
+        resource.write_bytes(gzip.compress(json.dumps(graph).encode(), mtime=0))
+        self.page.goto(self.base + 'graph.html')
+        self.choose_endpoint('source', 'Graph Partitioning')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('1 best route')
+        expect(self.page.locator('.path .size')).to_have_text('n⁹⁰⁰⁷¹⁹⁹²⁵⁴⁷⁴⁰⁹⁹³', timeout=1000)
+        summaries = self.page.locator('.growth').evaluate('''dl => Object.fromEntries(
+            [...dl.querySelectorAll('dt')].map(term => [term.textContent, term.nextElementSibling.textContent]))''')
+        self.assertEqual(summaries['vars'], 'Θ(vertices⁹⁰⁰⁷¹⁹⁹²⁵⁴⁷⁴⁰⁹⁹³)')
+        quadratic = summaries['quadratic terms']
+        self.assertRegex(quadratic, r'^Θ\([^()]+\)$')
+        # Product factors commute; their exact exponents and multiplicity must agree.
+        self.assertCountEqual(quadratic.removeprefix('Θ(').removesuffix(')').split('·'),
+                              ['edges⁹⁰⁰⁷¹⁹⁹²⁵⁴⁷⁴⁰⁹⁹²', 'vertices'])
+        route = self.copy_route()
+        self.assertEqual([step['to']['name'] for step in route['path']], ['QUBO'])
+
+    def cancel_pending_engine(self):
+        # Hold the real HTTP response so cancellation deterministically precedes path results.
+        self.engine_release.clear()
+        self.page.goto(self.base + 'graph.html')
+        self.assertTrue(self.engine_requested.wait(timeout=1), 'The real WASM request never started')
+        expect(self.page.locator('.path')).to_have_count(0)
+        self.page.get_by_role('button', name='Cancel', exact=True).click()
+        expect(self.page.locator('#results')).to_contain_text('Search cancelled.')
+        self.engine_release.set()
+
+    def test_graph_cancel_before_paths_allows_successful_retry(self):
+        self.cancel_pending_engine()
+        self.page.get_by_role('button', name='Search again', exact=True).click()
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.assertEqual(self.copy_route()['path'][-1]['to']['name'], 'QUBO')
+
+    def test_graph_recovers_after_offline_engine_start(self):
+        self.cancel_pending_engine()
+        self.context.set_offline(True)
+        self.page.get_by_role('button', name='Search again', exact=True).click()
+        expect(self.page.locator('#results')).to_contain_text('Cannot load the path engine')
+        expect(self.page.get_by_role('button', name='Cancel', exact=True)).to_have_count(0)
+        self.context.set_offline(False)
+        self.page.get_by_role('button', name='SAT → QUBO', exact=True).click()
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.assertEqual(self.copy_route()['path'][-1]['to']['name'], 'QUBO')
+
+    def assert_detail_recovery(self, resource, message):
+        original = resource.read_bytes()
+        resource.unlink()
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        def open_details():
+            self.page.locator('.scene-node[data-node="MaximumIndependentSet"]').click()
+            self.page.locator('#pop .pop-details').click()
+        open_details()
+        expect(self.page.locator('#drawer-body [role="alert"]')).to_contain_text(message)
+        expect(self.page.locator('#drawer-body [aria-busy="true"]')).to_have_count(0)
+        resource.write_bytes(original)
+        self.page.get_by_role('button', name='Close details', exact=True).click()
+        open_details()
+        expect(self.page.locator('#drawer-body article')).to_contain_text('wireless network scheduling')
+        expect(self.page.locator('#drawer-body [role="alert"]')).to_have_count(0)
+        self.assertEqual(self.copy_route()['path'][-1]['to']['name'], 'QUBO')
+
+    def test_graph_details_retry_after_missing_index(self):
+        self.assert_detail_recovery(self.assets / 'graph-details.json', 'Cannot load documentation index')
+
+    def test_graph_details_retry_after_missing_article(self):
+        manifest = json.loads((self.assets / 'graph-details.json').read_text())
+        article = self.site / manifest['entries']['problem:MaximumIndependentSet']
+        self.assert_detail_recovery(article, 'Cannot load documentation (404)')
+
+    def test_graph_details_rejects_index_urls_outside_current_articles_and_recovers(self):
+        resource = self.assets / 'graph-details.json'
+        original = resource.read_bytes()
+        manifest = json.loads(original)
+        manifest['entries']['problem:MaximumIndependentSet'] = './index.html'
+        resource.write_text(json.dumps(manifest))
+        self.page.goto(self.base + 'graph.html')
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        def open_details():
+            self.open_problem_popover('MaximumIndependentSet')
+            self.page.get_by_role('button', name='Details', exact=True).click()
+        open_details()
+        expect(self.page.locator('#drawer-body [role="alert"]')).to_contain_text('Invalid documentation index', timeout=1000)
+        resource.write_bytes(original)
+        self.page.get_by_role('button', name='Close details', exact=True).click()
+        open_details()
+        expect(self.page.locator('#drawer-body article')).to_contain_text('wireless network scheduling')
+        self.assertEqual(self.copy_route()['path'][-1]['to']['name'], 'QUBO')
+
+    def test_graph_scene_failure_releases_worker_and_reload_recovers(self):
+        resource = self.assets / 'graph-scene.json.gz'
+        original = resource.read_bytes()
+        resource.unlink()
+        # Let the eager worker start before delivering the scene's real 404 response.
+        self.scene_release.clear()
+        self.page.goto(self.base + 'graph.html')
+        self.assertTrue(self.engine_requested.wait(timeout=1), 'The eager engine never requested its WASM')
+        self.scene_release.set()
+        expect(self.page.locator('#results')).to_contain_text('Cannot load graph', timeout=1000)
+        deadline = time.monotonic() + 1
+        while self.page.workers and time.monotonic() < deadline:
+            self.page.wait_for_timeout(10)
+        self.assertEqual(self.page.workers, [], 'A failed graph retained its unused path worker')
+        resource.write_bytes(original)
+        self.page.reload()
+        expect(self.page.locator('#results .summary strong')).to_contain_text('best route')
+        self.assertEqual(self.copy_route()['path'][-1]['to']['name'], 'QUBO')
+
+
+def load_tests(loader, tests, pattern):
+    # Reuse browser fixtures without running the inherited page suite a second time.
+    return unittest.TestSuite(WebsiteFailureTests(name) for name in WebsiteFailureTests.__dict__ if name.startswith('test_'))
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/scripts/test_website_growth.mjs b/scripts/test_website_growth.mjs
new file mode 100644
index 000000000..e1b4be397
--- /dev/null
+++ b/scripts/test_website_growth.mjs
@@ -0,0 +1,40 @@
+import assert from 'node:assert/strict';
+import { test } from 'node:test';
+import { growth, pathDegree, sizeBadge, compareDegrees } from '../docs/website/src/lib/graph-growth.mts';
+
+const field = (certificate, kind = 'exact') => ({ certificate, accuracy: { kind } });
+
+test('growth distinguishes adjacent wide powers when selecting leading terms', () => {
+  const value = field('num_edges^9007199254740992 + num_vertices^9007199254740993');
+  assert.deepEqual(growth(value), { degree: 9007199254740993n, lead: 'Θ(vertices⁹⁰⁰⁷¹⁹⁹²⁵⁴⁷⁴⁰⁹⁹³)' });
+  assert.equal(value.certificate, 'num_edges^9007199254740992 + num_vertices^9007199254740993');
+  assert.equal(sizeBadge(pathDegree({ fields: { size: value } })), 'n⁹⁰⁰⁷¹⁹⁹²⁵⁴⁷⁴⁰⁹⁹³');
+});
+
+test('growth sums large monomial exponents without rounding or changing rational coefficients', () => {
+  const value = field('9007199254740993 * 7^-1 * num_edges^9007199254740993 * num_vertices');
+  const original = structuredClone(value);
+  assert.deepEqual(growth(value), { degree: 9007199254740994n, lead: 'Θ(edges⁹⁰⁰⁷¹⁹⁹²⁵⁴⁷⁴⁰⁹⁹³·vertices)' });
+  assert.deepEqual(value, original);
+  assert.equal(growth(field('num_vertices^123456789012345678901234567890')).degree, 123456789012345678901234567890n);
+});
+
+test('growth retains constants, bounds, empty profiles and unavailable fields', () => {
+  assert.deepEqual(growth(field('2 * num_edges^2 + 3^-1 * num_vertices^2 + 1', 'upper_bound')),
+    { degree: 2n, lead: 'O(edges² + vertices²)' });
+  assert.equal(sizeBadge(pathDegree({ fields: { size: field('9007199254740993 * 3^-1') } })), '1');
+  assert.equal(sizeBadge(pathDegree({ fields: {} })), '1');
+  assert.equal(sizeBadge(pathDegree({ fields: { size: field('num_vertices') } })), 'n');
+  assert.equal(pathDegree({ fields: { known: field('num_vertices'), missing: field(null, 'unavailable') } }), null);
+  assert.deepEqual(growth(field(null, 'unavailable')), { degree: null, lead: 'unavailable' });
+  assert.equal(sizeBadge(null), '?');
+});
+
+test('degree ordering retains exact comparisons, ties and unavailable-last behavior', () => {
+  assert.equal(compareDegrees(9007199254740993n, 9007199254740992n), 1);
+  assert.equal(compareDegrees(9007199254740992n, 9007199254740993n), -1);
+  assert.equal(compareDegrees(9007199254740993n, 9007199254740993n), 0);
+  assert.equal(compareDegrees(null, 0n), 1);
+  assert.equal(compareDegrees(0n, undefined), -1);
+  assert.equal(compareDegrees(null, undefined), 0);
+});
diff --git a/scripts/test_website_verification.py b/scripts/test_website_verification.py
new file mode 100644
index 000000000..82095262f
--- /dev/null
+++ b/scripts/test_website_verification.py
@@ -0,0 +1,193 @@
+"""Fresh artifact verification uses real files, HTTP, and browser requests."""
+
+from pathlib import Path
+from contextlib import redirect_stderr
+import io
+import os
+import json
+import shutil
+import subprocess
+import socket
+import struct
+import sys
+import tempfile
+import unittest
+from urllib.request import build_opener, ProxyHandler
+from urllib.parse import urlsplit
+
+from check_website import prepare_output, serve_website, write_provenance
+import check_website
+
+
+class WebsiteVerificationTests(unittest.TestCase):
+    def test_source_changes_invalidate_the_verification_snapshot(self):
+        with tempfile.TemporaryDirectory() as directory:
+            root = Path(directory)
+            subprocess.run(['git', 'init', '-q', str(root)], check=True)
+            source = root / 'source.txt'
+            source.write_text('original')
+            subprocess.run(['git', '-C', str(root), 'add', 'source.txt'], check=True)
+            subprocess.run(['git', '-C', str(root), '-c', 'user.name=Test', '-c', 'user.email=test@example.org',
+                            'commit', '-qm', 'Initial source'], check=True)
+            before = check_website.source_state(root)
+            check_website.verify_source_unchanged(before, root)
+            source.write_text('changed')
+            with self.assertRaises(ValueError):
+                check_website.verify_source_unchanged(before, root)
+            source.write_text('original')
+            (root / 'new-source.txt').write_text('new source')
+            with self.assertRaises(ValueError):
+                check_website.verify_source_unchanged(before, root)
+
+    def test_output_inside_checkout_is_excluded_from_source_comparison(self):
+        with tempfile.TemporaryDirectory() as directory:
+            root = Path(directory)
+            subprocess.run(['git', 'init', '-q', str(root)], check=True)
+            (root / 'source.txt').write_text('source')
+            subprocess.run(['git', '-C', str(root), 'add', 'source.txt'], check=True)
+            subprocess.run(['git', '-C', str(root), '-c', 'user.name=Test', '-c', 'user.email=test@example.org',
+                            'commit', '-qm', 'Initial source'], check=True)
+            output = root / 'output'
+            before = check_website.source_state(root, output)
+            output.mkdir()
+            (output / 'index.html').write_text('built artifact')
+            check_website.verify_source_unchanged(before, root, output)
+
+    def test_canceled_asset_request_does_not_print_a_server_traceback(self):
+        with tempfile.TemporaryDirectory() as directory:
+            site = Path(directory)
+            (site / "large.bin").write_bytes(b"x" * (8 * 1024 * 1024))
+            errors = io.StringIO()
+            with redirect_stderr(errors), serve_website(site) as base:
+                target = urlsplit(base)
+                with socket.create_connection((target.hostname, target.port), timeout=2) as client:
+                    client.sendall(b"GET /large.bin HTTP/1.0\r\nHost: localhost\r\n\r\n")
+                    headers = b""
+                    while b"\r\n\r\n" not in headers:
+                        chunk = client.recv(1024)
+                        self.assertTrue(chunk)
+                        headers += chunk
+                    self.assertIn(b"200 OK", headers)
+                    client.setsockopt(socket.SOL_SOCKET, socket.SO_LINGER, struct.pack("ii", 1, 0))
+            self.assertEqual(errors.getvalue(), "")
+
+    def test_verification_only_report_does_not_claim_the_artifact_build_source(self):
+        with tempfile.TemporaryDirectory() as directory:
+            site = Path(directory)
+            with self.assertRaises(FileNotFoundError):
+                check_website.check(site, build=False, open_questions=None)
+            report = json.loads((site / "verification.json").read_text())
+            self.assertEqual(report["verification"]["status"], "failed")
+            self.assertEqual(report["verification"]["mode"], "existing_artifact")
+            self.assertEqual(report["verification"]["source_role"], "verifier_only")
+
+    def test_missing_tools_fail_before_creating_output(self):
+        with tempfile.TemporaryDirectory() as directory:
+            output = Path(directory) / "new-output"
+            result = subprocess.run([sys.executable, str(Path(check_website.__file__)), "--output", str(output)],
+                                    env={**os.environ, "PATH": "", "CARGO_HOME": directory},
+                                    capture_output=True, text=True)
+            self.assertEqual(result.returncode, 2)
+            self.assertFalse(output.exists())
+            self.assertIn("mdbook", result.stderr)
+            self.assertIn("wasm-bindgen", result.stderr)
+            self.assertNotIn("Traceback", result.stderr)
+
+    def test_cargo_bin_fallback_preserves_the_active_cargo(self):
+        environment = dict(os.environ)
+        active_cargo = shutil.which("cargo", path=environment["PATH"])
+        self.assertIsNotNone(active_cargo)
+        environment.pop("CARGO_HOME", None)
+        path = check_website.tool_path(environment)
+        self.assertIn(str(Path.home() / ".cargo/bin"), path.split(os.pathsep))
+        self.assertEqual(shutil.which("cargo", path=path), active_cargo)
+
+    def test_configured_cargo_bin_runs_real_executables(self):
+        interpreter = Path(sys.executable).resolve()
+        environment = {**os.environ, "PATH": "", "CARGO_HOME": str(interpreter.parent.parent)}
+        environment["PATH"] = check_website.tool_path(environment)
+        result = subprocess.run([interpreter.name, "-c", "print(6 * 7)"],
+                                env=environment, check=True, capture_output=True, text=True)
+        self.assertEqual(result.stdout.strip(), "42")
+
+    def test_existing_output_is_preserved_and_refused(self):
+        with tempfile.TemporaryDirectory() as directory:
+            output = Path(directory) / "existing"
+            output.mkdir()
+            marker = output / "index.html"
+            marker.write_text("previous build")
+            with self.assertRaises(FileExistsError):
+                prepare_output(output)
+            self.assertEqual(marker.read_text(), "previous build")
+            fresh = prepare_output(Path(directory) / "fresh")
+            self.assertTrue(fresh.is_dir())
+            self.assertEqual(list(fresh.iterdir()), [])
+
+    def test_server_serves_selected_artifact_and_closes_after_failure(self):
+        direct = build_opener(ProxyHandler({}))
+        with tempfile.TemporaryDirectory() as directory:
+            site = Path(directory)
+            (site / "index.html").write_text("selected artifact")
+            with self.assertRaisesRegex(RuntimeError, "verification failed"):
+                with serve_website(site) as base:
+                    self.assertEqual(direct.open(base, timeout=1).read(), b"selected artifact")
+                    raise RuntimeError("verification failed")
+            with self.assertRaises(OSError):
+                direct.open(base, timeout=1)
+
+    def test_provenance_fingerprints_artifact_bytes(self):
+        with tempfile.TemporaryDirectory() as directory:
+            site = Path(directory)
+            (site / "index.html").write_bytes(b"abc")
+            evidence = write_provenance(site, {"result": "passed"})
+            self.assertEqual(evidence["artifacts"]["index.html"],
+                             "ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad")
+            self.assertEqual(evidence["verification"], {"result": "passed"})
+
+    def test_baseline_inputs_must_match_the_verified_artifact(self):
+        with tempfile.TemporaryDirectory() as directory:
+            site = Path(directory)
+            page = site / "index.html"
+            page.write_text("verified contents")
+            write_provenance(site, {"status": "passed"})
+            self.assertIn("index.html", check_website.verified_artifact(site)["artifacts"])
+            page.write_text("changed after verification")
+            with self.assertRaises(ValueError):
+                check_website.verified_artifact(site)
+
+    def test_baseline_rejects_failed_reports_and_external_paths(self):
+        with tempfile.TemporaryDirectory() as directory:
+            root = Path(directory)
+            site = root / "site"
+            site.mkdir()
+            (site / "index.html").write_text("abc")
+            write_provenance(site, {"status": "failed"})
+            with self.assertRaises(ValueError):
+                check_website.verified_artifact(site)
+            (root / "outside").write_text("abc")
+            report = write_provenance(site, {"status": "passed"})
+            report["artifacts"] = {"../outside": report["artifacts"]["index.html"]}
+            (site / "verification.json").write_text(json.dumps(report))
+            with self.assertRaises(ValueError):
+                check_website.verified_artifact(site)
+
+    def test_nested_checkout_is_recorded_without_hashing_a_directory(self):
+        root = Path(__file__).resolve().parents[1]
+        with tempfile.TemporaryDirectory(prefix="verification-checkout-", dir=root) as checkout:
+            subprocess.run(["git", "init", "--quiet", checkout], check=True)
+            (Path(checkout) / "README.md").write_text("separately built source")
+            with tempfile.TemporaryDirectory() as directory:
+                evidence = write_provenance(Path(directory), {"result": "passed"})
+            self.assertIn(Path(checkout).name + "/", evidence["nested_checkouts"])
+            self.assertIsNone(evidence["nested_checkouts"][Path(checkout).name + "/"])
+            subprocess.run(["git", "-C", checkout, "-c", "user.name=Fixture",
+                            "-c", "user.email=fixture@example.invalid", "-c", "commit.gpgsign=false",
+                            "-c", "core.hooksPath=/dev/null", "commit", "--quiet", "--allow-empty", "-m", "Source snapshot"], check=True)
+            expected = subprocess.check_output(["git", "-C", checkout, "log", "-1", "--format=%H"], text=True).strip()
+            with tempfile.TemporaryDirectory() as directory:
+                evidence = write_provenance(Path(directory), {"result": "passed"})
+            self.assertEqual(evidence["nested_checkouts"][Path(checkout).name + "/"], expected)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/scripts/validate_website_data.mjs b/scripts/validate_website_data.mjs
new file mode 100644
index 000000000..f3103b320
--- /dev/null
+++ b/scripts/validate_website_data.mjs
@@ -0,0 +1,18 @@
+import { validateNativeExportData, validateAtlasSummary, validateAtlasRecord,
+  validateGraphSceneData, validateDetailsIndexData, validatePathGraphData } from './website_contracts.mjs';
+import { readFileSync } from 'node:fs';
+
+/** @type {unknown} */
+const value = JSON.parse(readFileSync(0, 'utf8'));
+switch (process.argv[2]) {
+  case 'native-exports': validateNativeExportData(value); break;
+  case 'atlas-summary': validateAtlasSummary(value); break;
+  case 'atlas-records':
+    if (!Array.isArray(value)) throw new Error('Expected an array of Atlas records');
+    for (const record of value) validateAtlasRecord(record);
+    break;
+  case 'graph-scene': validateGraphSceneData(value); break;
+  case 'path-graph': validatePathGraphData(value); break;
+  case 'graph-details': validateDetailsIndexData(value, new URL(process.argv[3]), new URL(process.argv[4])); break;
+  default: throw new Error('Usage: node scripts/validate_website_data.mjs native-exports | atlas-summary | atlas-records | graph-scene | path-graph | graph-details PAGE_URL ARTICLES_URL < DATA');
+}
diff --git a/scripts/website-requirements.txt b/scripts/website-requirements.txt
new file mode 100644
index 000000000..b8b152ad0
--- /dev/null
+++ b/scripts/website-requirements.txt
@@ -0,0 +1,4 @@
+playwright==1.58.0
+pyee==13.0.1
+greenlet==3.5.6
+typing_extensions==4.16.0
diff --git a/scripts/website_contracts.mjs b/scripts/website_contracts.mjs
new file mode 100644
index 000000000..f78fb0e52
--- /dev/null
+++ b/scripts/website_contracts.mjs
@@ -0,0 +1,197 @@
+import {readFileSync} from 'node:fs';
+import Ajv2020 from 'ajv/dist/2020.js';
+import {validateDetailURL} from '../docs/website/src/lib/graph-details-data.mts';
+import {nodeKey} from '../docs/website/src/lib/variant.mts';
+
+const root = new URL('../docs/website/', import.meta.url);
+const wasmSchemas = JSON.parse(readFileSync(new URL('src/generated/wasm-schemas.json', root), 'utf8'));
+const ajv = new Ajv2020({strict: true});
+function validator(name) {
+  return ajv.compile(wasmSchemas[name] ?? JSON.parse(readFileSync(new URL(name + '.schema.json', root), 'utf8')));
+}
+
+const validateAtlas = validator('atlas-data');
+const validateGraphScene = validator('graph-scene');
+const validateGraphDetails = validator('graph-details');
+const validatePathGraph = validator('path-graph');
+const validateNativeExports = validator('native-exports');
+const validateWasmPaths = validator('wasm-paths');
+const validateWasmComparison = validator('wasm-comparison');
+export const validateWasmPathRequest = validator('wasm-path-request');
+export const validateWasmComparisonRequest = validator('wasm-comparison-request');
+
+export function validateGraphReferences(data, error) {
+    if (new Set(data.nodes.map(nodeKey)).size !== data.nodes.length)
+        throw error?.() ?? new Error('Duplicate graph variant.');
+    if (data.edges.some(edge => !data.nodes[edge.source] || !data.nodes[edge.target]))
+        throw error?.() ?? new Error('Graph edge references an unknown variant.');
+}
+
+const error = () => new Error('Invalid atlas data. Reload the current release and try again.');
+export function validateAtlasSummary(value) {
+    if (!validateAtlas(value) || value.kind !== 'summary')
+        throw error();
+    validateGraphReferences(value, error);
+    const families = new Set(value.nodes.map(node => node.name));
+    if (value.schemas.length !== families.size || new Set(value.schemas.map(schema => schema.name)).size !== families.size
+        || value.schemas.some(schema => !families.has(schema.name)))
+        throw error();
+    return value;
+}
+export function validateAtlasRecord(value, family) {
+    if (!validateAtlas(value) || value.kind !== 'record')
+        throw error();
+    validateGraphReferences(value, error);
+    const schema = value.schemas[0];
+    if ((family !== undefined && schema.name !== family) || !value.nodes.some(node => node.name === schema.name)
+        || value.nodes.some(node => node.name === schema.name && node.category !== schema.category)
+        || value.edges.some(edge => value.nodes[edge.source].name !== schema.name && value.nodes[edge.target].name !== schema.name))
+        throw error();
+    return value;
+}
+
+export function validateGraphSceneData(value) {
+    if (!validateGraphScene(value))
+        throw new Error('Invalid graph scene contract. Reload the current release.');
+    const families = new Set(value.nodes.map(node => node.name));
+    const defaults = new Map();
+    for (const node of value.nodes)
+        if (node.default)
+            defaults.set(node.name, (defaults.get(node.name) ?? 0) + 1);
+    if ([...families].some(name => defaults.get(name) !== 1))
+        throw new Error('Each graph family needs exactly one default.');
+    validateGraphReferences(value);
+    if (Object.keys(value.aliases).some(name => !families.has(name)))
+        throw new Error('Graph alias references an unknown family.');
+    if (Object.keys(value.layout).length !== families.size || Object.keys(value.layout).some(name => !families.has(name))) {
+        throw new Error('Graph layout must cover exactly the registered families.');
+    }
+    return value;
+}
+
+export function validatePathGraphData(value) {
+    if (!validatePathGraph(value))
+        throw new Error('Invalid path metadata contract. Reload the current release.');
+    validatePathGraphReferences(value);
+    return value;
+}
+export function validatePathGraphReferences(value) {
+    const error = () => new Error('Invalid path metadata contract. Reload the current release.');
+    validateGraphReferences(value, error);
+    const defaults = new Map();
+    for (const node of value.nodes)
+        defaults.set(node.name, (defaults.get(node.name) ?? 0) + (node.default ? 1 : 0));
+    if ([...defaults.values()].some(count => count !== 1))
+        throw error();
+    const edges = new Set();
+    for (const edge of value.edges) {
+        const target = value.nodes[edge.target];
+        const key = `${edge.source}:${edge.target}`;
+        if (edges.has(key))
+            throw error();
+        edges.add(key);
+        const fields = new Set(edge.parameters.map(parameter => parameter.field));
+        if (fields.size !== edge.parameters.length || [...fields].some(field => !target.parameter_names.includes(field))
+            || (edge.parameter_contract_error === null && fields.size !== target.parameter_names.length))
+            throw error();
+    }
+}
+
+export function validateNativeExportData(value) {
+    const error = () => new Error('Invalid native registry exports. Regenerate graph and problem schemas together.');
+    if (!validateNativeExports(value))
+        throw error();
+    validatePathGraphReferences(value.graph);
+    const families = new Set(value.graph.nodes.map(node => node.name));
+    const schemas = new Map(value.schemas.map(schema => [schema.name, schema]));
+    if (schemas.size !== value.schemas.length || schemas.size !== families.size
+        || [...schemas.keys()].some(name => !families.has(name))
+        || Object.keys(value.graph.aliases).some(name => !families.has(name))
+        || value.graph.nodes.some(node => schemas.get(node.name)?.category !== node.category))
+        throw error();
+    return value;
+}
+
+function sameEndpoint(left, right) {
+    const entries = Object.entries(left.variant);
+    return left.name === right.name && entries.length === Object.keys(right.variant).length
+        && entries.every(([key, value]) => Object.hasOwn(right.variant, key) && right.variant[key] === value);
+}
+export function parseWasmPathResult(text) {
+    const value = JSON.parse(text);
+    return validateWasmPathResultData(value);
+}
+export function validateWasmPathResultData(value) {
+    const error = () => new Error('Invalid path result contract. Reload the current release.');
+    if (!validateWasmPaths(value))
+        throw error();
+    if (value.truncated && !value.paths.length)
+        throw error();
+    for (const route of value.paths) {
+        if (route.steps !== route.path.length)
+            throw error();
+        let previous;
+        for (const step of route.path) {
+            if (previous && !sameEndpoint(previous, step.from))
+                throw error();
+            previous = step.to;
+        }
+    }
+    return value;
+}
+
+export function validateComparisonParameters(value, source, target) {
+    const coordinates = new Set(source), fields = new Set(target);
+    for (const profile of value.profiles) {
+        const names = Object.keys(profile.fields);
+        if (new Set(profile.source_coordinates).size !== coordinates.size
+            || profile.source_coordinates.some(name => !coordinates.has(name))
+            || names.length !== fields.size || names.some(name => !fields.has(name))) {
+            throw new Error('Comparison parameters do not match the registered endpoints. Reload the current release.');
+        }
+    }
+}
+export function parseWasmComparison(text, pathCount) {
+    const value = JSON.parse(text);
+    return validateWasmComparisonData(value, pathCount);
+}
+export function validateWasmComparisonData(value, pathCount) {
+    const error = () => new Error('Invalid comparison result contract. Reload the current release.');
+    if (!Number.isSafeInteger(pathCount) || pathCount < 0 || !validateWasmComparison(value))
+        throw error();
+    if (value.profiles.length !== pathCount)
+        throw error();
+    const total = BigInt(pathCount) * (BigInt(pathCount) - 1n) / 2n;
+    if (Object.values(value.counts).reduce((sum, count) => sum + BigInt(count), 0n) !== total)
+        throw error();
+    const front = new Set(value.front);
+    if (front.size !== value.front.length || (pathCount > 0 && !front.size)
+        || value.front.some(index => index > pathCount))
+        throw error();
+    for (const profile of value.profiles) {
+        const coordinates = new Set(profile.source_coordinates);
+        if (coordinates.size !== profile.source_coordinates.length)
+            throw error();
+        for (const field of Object.values(profile.fields)) {
+            if ((field.certificate === null) !== (field.accuracy.kind === 'unavailable'))
+                throw error();
+            if (field.certificate !== null)
+                for (const variable of field.certificate.matchAll(/[A-Za-z_]\w*/g)) {
+                    if (!coordinates.has(variable[0]))
+                        throw error();
+                }
+        }
+    }
+    return value;
+}
+
+export function validateDetailsIndexData(value, page, articles) {
+    const error = () => new Error('Invalid documentation index. Reload the current release.');
+    if (!validateGraphDetails(value))
+        throw error();
+    for (const entry of Object.values(value.entries))
+        validateDetailURL(entry, page, articles);
+    if (Object.values(value.anchors).some(key => !Object.hasOwn(value.entries, key)))
+        throw error();
+    return value;
+}
diff --git a/src/lib.rs b/src/lib.rs
index 1c70132cb..8155d46ec 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -32,14 +32,16 @@ pub mod growth;
 pub mod io;
 pub mod models;
 pub mod parameters;
+mod path_search;
+pub mod poly_compare;
+pub mod polynomial;
+mod problem_parameters;
 pub mod random;
 pub mod registry;
 pub mod rules;
 pub mod solvers;
 pub mod topology;
 pub mod traits;
-#[allow(dead_code)]
-pub(crate) mod truth_table;
 pub mod types;
 pub mod variant;
 
diff --git a/src/models/misc/factoring.rs b/src/models/misc/factoring.rs
index eae8f35da..5cd030f78 100644
--- a/src/models/misc/factoring.rs
+++ b/src/models/misc/factoring.rs
@@ -203,20 +203,6 @@ fn bits_to_biguint(bits: &[usize]) -> BigUint {
         })
 }
 
-/// Convert an integer to a bit vector (little-endian).
-#[allow(dead_code)]
-fn int_to_bits(n: &BigUint, num_bits: usize) -> Vec<usize> {
-    (0..num_bits)
-        .map(|index| usize::from(n.bit(u64::try_from(index).expect("bit index fits u64"))))
-        .collect()
-}
-
-/// Check if the given factors correctly factorize the target.
-#[cfg(test)]
-pub(crate) fn is_factoring(target: &BigUint, a: &BigUint, b: &BigUint) -> bool {
-    a * b == *target
-}
-
 impl Problem for Factoring {
     const NAME: &'static str = "Factoring";
     type Solution = (BigUint, BigUint);
diff --git a/src/parameters.rs b/src/parameters.rs
index 0ab7a513d..8b3763982 100644
--- a/src/parameters.rs
+++ b/src/parameters.rs
@@ -1,6 +1,7 @@
 //! Symbolic parameter transformations carried by reduction rules.
 
 use crate::expr::{AlgebraicAnalysis, Expr, ExprNode, ExprNodeId, Symbol};
+use crate::polynomial::{pow_rational, Poly};
 use crate::types::ProblemParameters;
 use num_bigint::{BigInt, BigUint, Sign};
 use num_rational::BigRational;
@@ -150,6 +151,13 @@ impl ParameterTransform {
         );
     }
 
+    /// Declared or propagated unavailable target fields.
+    pub fn unavailable_fields(&self) -> impl Iterator<Item = (&str, &ParameterTransformError)> {
+        self.unavailable
+            .iter()
+            .map(|(name, reason)| (name.as_ref(), reason))
+    }
+
     pub fn expressions(&self) -> impl Iterator<Item = (&str, &Expr)> {
         self.fields
             .iter()
@@ -213,29 +221,47 @@ impl ParameterTransform {
         let mut unavailable = next.unavailable.clone();
         for field in &next.fields {
             let result = (|| {
-                let mut bounded_input = false;
-                for input in field.expression.variables() {
+                // Expansion exposes cancelled dependencies: `n + m - m` no longer reads `m`.
+                let poly = Poly::from_expr(&field.expression);
+                let inputs: Vec<Box<str>> = match &poly {
+                    Some(poly) => poly.variables().iter().map(|v| v.as_str().into()).collect(),
+                    None => field
+                        .expression
+                        .variables()
+                        .into_iter()
+                        .map(Into::into)
+                        .collect(),
+                };
+                let mut bounded = HashSet::new();
+                for input in &inputs {
                     if let Some(cause) = self.unavailable(input) {
                         return Err(ParameterTransformError::UnavailableInput {
                             edge: next.edge.clone(),
                             field: field.name.clone(),
-                            input_field: input.into(),
+                            input_field: input.as_ref().into(),
                             cause: Box::new(cause.clone()),
                         });
                     }
-                    bounded_input |= self.relation(input) == Some(ParameterRelation::UpperBound);
+                    if self.relation(input) == Some(ParameterRelation::UpperBound) {
+                        bounded.insert(input.as_ref());
+                    }
                 }
-                let expression = if bounded_input {
-                    positive_polynomial_hull(&field.expression).ok_or_else(|| {
-                        ParameterTransformError::CannotPropagateUpperBound {
+                // Partial hull: keep a negative term only when all its variables are exact,
+                // so the formula is monotone in every upper-bounded input.
+                let expression = match poly {
+                    Some(poly) => poly
+                        .hull(|m| m.keys().all(|v| !bounded.contains(v.as_str())))
+                        .to_expr(),
+                    None if bounded.is_empty() => field.expression.clone(),
+                    None => {
+                        return Err(ParameterTransformError::CannotPropagateUpperBound {
                             edge: next.edge.clone(),
                             field: field.name.clone(),
                             expression: field.expression.to_string().into(),
-                        }
-                    })?
-                } else {
-                    field.expression.clone()
+                        })
+                    }
                 };
+                let bounded_input = !bounded.is_empty();
                 let expression =
                     expression
                         .substitute_complete(&replacements)
@@ -264,102 +290,6 @@ impl ParameterTransform {
     }
 }
 
-type Monomial = BTreeMap<Symbol, BigUint>;
-type Polynomial = BTreeMap<Monomial, BigRational>;
-
-fn positive_polynomial_hull(expression: &Expr) -> Option<Expr> {
-    let polynomial = polynomial(expression)?;
-    let terms = polynomial
-        .into_iter()
-        .filter(|(_, coefficient)| coefficient.is_positive())
-        .map(|(monomial, coefficient)| {
-            monomial
-                .into_iter()
-                .fold(Expr::constant(coefficient), |term, (variable, exponent)| {
-                    term * Expr::pow(
-                        Expr::variable(variable.as_str()),
-                        Expr::integer(BigInt::from(exponent)),
-                    )
-                })
-        });
-    Some(terms.fold(Expr::integer(0), |sum, term| sum + term))
-}
-
-fn polynomial(expression: &Expr) -> Option<Polynomial> {
-    match expression.node() {
-        ExprNode::Const(value) => Some(BTreeMap::from([(BTreeMap::new(), value.clone())])),
-        ExprNode::Var(variable) => Some(BTreeMap::from([(
-            BTreeMap::from([(variable.clone(), BigUint::one())]),
-            BigRational::one(),
-        )])),
-        ExprNode::Add(values) => values.iter().try_fold(BTreeMap::new(), |sum, value| {
-            Some(add_polynomials(sum, polynomial(value)?))
-        }),
-        ExprNode::Mul(values) => values.iter().try_fold(
-            BTreeMap::from([(BTreeMap::new(), BigRational::one())]),
-            |product, value| Some(multiply_polynomials(product, polynomial(value)?)),
-        ),
-        ExprNode::Pow(base, exponent) => {
-            let ExprNode::Const(exponent) = exponent.node() else {
-                return None;
-            };
-            if !exponent.is_integer() {
-                return None;
-            }
-            if exponent.is_negative() {
-                let ExprNode::Const(base) = base.node() else {
-                    return None;
-                };
-                if base.is_zero() {
-                    return None;
-                }
-                return Some(BTreeMap::from([(
-                    BTreeMap::new(),
-                    pow_rational(base.clone(), &exponent.to_integer()),
-                )]));
-            }
-            let mut exponent = exponent.to_integer().magnitude().clone();
-            let mut base = polynomial(base)?;
-            let mut result = BTreeMap::from([(BTreeMap::new(), BigRational::one())]);
-            while !exponent.is_zero() {
-                if exponent.bit(0) {
-                    result = multiply_polynomials(result, base.clone());
-                }
-                exponent >>= 1usize;
-                if !exponent.is_zero() {
-                    base = multiply_polynomials(base.clone(), base);
-                }
-            }
-            Some(result)
-        }
-        ExprNode::Exp(_) | ExprNode::Log(_) | ExprNode::Factorial(_) => None,
-    }
-}
-
-fn add_polynomials(mut left: Polynomial, right: Polynomial) -> Polynomial {
-    for (monomial, right_coefficient) in right {
-        *left.entry(monomial).or_insert_with(BigRational::zero) += right_coefficient;
-    }
-    left.retain(|_, coefficient| !coefficient.is_zero());
-    left
-}
-
-fn multiply_polynomials(left: Polynomial, right: Polynomial) -> Polynomial {
-    let mut product = Polynomial::new();
-    for (left_monomial, left_coefficient) in left {
-        for (right_monomial, right_coefficient) in &right {
-            let mut monomial = left_monomial.clone();
-            for (variable, exponent) in right_monomial {
-                *monomial.entry(variable.clone()).or_default() += exponent;
-            }
-            *product.entry(monomial).or_insert_with(BigRational::zero) +=
-                &left_coefficient * right_coefficient;
-        }
-    }
-    product.retain(|_, coefficient| !coefficient.is_zero());
-    product
-}
-
 fn compile(
     expression: &Expr,
     analysis: &AlgebraicAnalysis,
@@ -444,26 +374,6 @@ fn evaluate_plan(
     Ok(value)
 }
 
-fn pow_rational(mut base: BigRational, exponent: &BigInt) -> BigRational {
-    let negative = exponent.sign() == Sign::Minus;
-    let mut exponent = exponent.magnitude().clone();
-    let mut result = BigRational::one();
-    while !exponent.is_zero() {
-        if exponent.bit(0) {
-            result *= &base;
-        }
-        exponent >>= 1usize;
-        if !exponent.is_zero() {
-            base = &base * &base;
-        }
-    }
-    if negative {
-        result.recip()
-    } else {
-        result
-    }
-}
-
 fn ceil_nonnegative(value: &BigRational) -> BigUint {
     ((value.numer() + value.denom() - BigInt::one()) / value.denom())
         .magnitude()
diff --git a/src/path_search.rs b/src/path_search.rs
new file mode 100644
index 000000000..3e0492011
--- /dev/null
+++ b/src/path_search.rs
@@ -0,0 +1,118 @@
+//! Deterministic bounded Yen search shared by the registry and browser.
+use std::collections::{BTreeSet, HashMap, HashSet, VecDeque};
+
+fn shortest_path(
+    source: usize,
+    target: usize,
+    adjacency: &[Vec<usize>],
+    excluded_nodes: &HashSet<usize>,
+    excluded_edges: &HashSet<(usize, usize)>,
+    max_nodes: usize,
+) -> Option<Vec<usize>> {
+    if excluded_nodes.contains(&source) || max_nodes == 0 {
+        return None;
+    }
+    if source == target {
+        return Some(vec![source]);
+    }
+
+    let mut queue = VecDeque::from([(source, 1usize)]);
+    let mut parents = HashMap::new();
+    let mut visited = HashSet::from([source]);
+
+    while let Some((current, path_nodes)) = queue.pop_front() {
+        if path_nodes == max_nodes {
+            continue;
+        }
+        for &next in &adjacency[current] {
+            if excluded_nodes.contains(&next)
+                || excluded_edges.contains(&(current, next))
+                || !visited.insert(next)
+            {
+                continue;
+            }
+            parents.insert(next, current);
+            if next == target {
+                let mut path = vec![target];
+                let mut node = target;
+                while node != source {
+                    node = parents[&node];
+                    path.push(node);
+                }
+                path.reverse();
+                return Some(path);
+            }
+            queue.push_back((next, path_nodes + 1));
+        }
+    }
+    None
+}
+
+pub(crate) fn find_paths(
+    adjacency: &[Vec<usize>],
+    order: &[usize],
+    source: usize,
+    target: usize,
+    limit: usize,
+    max_nodes: usize,
+) -> Vec<Vec<usize>> {
+    if source == target || limit == 0 {
+        return Vec::new();
+    }
+    let Some(first) = shortest_path(
+        source,
+        target,
+        adjacency,
+        &HashSet::new(),
+        &HashSet::new(),
+        max_nodes,
+    ) else {
+        return Vec::new();
+    };
+
+    let mut accepted = vec![first];
+    let mut candidates = BTreeSet::new();
+
+    while accepted.len() < limit {
+        let previous = accepted.last().expect("accepted path exists");
+        for spur_index in 0..previous.len().saturating_sub(1) {
+            let root = &previous[..=spur_index];
+            let excluded_edges = accepted
+                .iter()
+                .filter(|path| path.len() > spur_index + 1 && path[..=spur_index] == *root)
+                .map(|path| (path[spur_index], path[spur_index + 1]))
+                .collect::<HashSet<_>>();
+            let excluded_nodes = root[..spur_index].iter().copied().collect();
+            let max_spur_nodes = max_nodes.saturating_sub(spur_index);
+            let Some(spur) = shortest_path(
+                previous[spur_index],
+                target,
+                adjacency,
+                &excluded_nodes,
+                &excluded_edges,
+                max_spur_nodes,
+            ) else {
+                continue;
+            };
+            let mut candidate = root[..spur_index].to_vec();
+            candidate.extend(spur);
+            if !accepted.contains(&candidate) {
+                let key = (
+                    candidate.len(),
+                    candidate
+                        .iter()
+                        .map(|&node| order[node])
+                        .collect::<Vec<_>>(),
+                );
+                candidates.insert((key, candidate));
+            }
+        }
+
+        let Some((_, next)) = candidates.pop_first() else {
+            break;
+        };
+        accepted.push(next);
+    }
+
+    accepted
+}
diff --git a/src/poly_compare/lp.rs b/src/poly_compare/lp.rs
new file mode 100644
index 000000000..7d60ff006
--- /dev/null
+++ b/src/poly_compare/lp.rs
@@ -0,0 +1,85 @@
+//! Exact Fourier–Motzkin feasibility with back substitution and a finite work cap.
+use super::*;
+
+/// Find nonnegative x with A x <= b; every returned point is checked against A,b.
+pub(super) fn feasible(
+    a: &[Vec<BigRational>],
+    b: &[BigRational],
+) -> Result<Option<Vec<BigRational>>, Reason> {
+    let n = a.first().map_or(0, Vec::len);
+    if n > 24 {
+        return Err(Reason::ResourceLimit("exact LP variables"));
+    }
+    let mut rows: Vec<_> = a.iter().cloned().zip(b.iter().cloned()).collect();
+    for i in 0..n {
+        let mut row = vec![BigRational::zero(); n];
+        row[i] = -BigRational::one();
+        rows.push((row, BigRational::zero()));
+    }
+    let mut stages = Vec::new();
+    for k in (0..n).rev() {
+        let positive: Vec<_> = rows.iter().filter(|(r, _)| r[k].is_positive()).collect();
+        let negative: Vec<_> = rows.iter().filter(|(r, _)| r[k].is_negative()).collect();
+        if positive.len().saturating_mul(negative.len()) + rows.len() > 512 {
+            return Err(Reason::ResourceLimit("exact LP elimination rows"));
+        }
+        let mut next: BTreeMap<Vec<BigRational>, BigRational> = BTreeMap::new();
+        let mut tighten = |row: Vec<BigRational>, rhs: BigRational| {
+            next.entry(row)
+                .and_modify(|v| *v = v.clone().min(rhs.clone()))
+                .or_insert(rhs);
+        };
+        for (r, b) in rows.iter().filter(|(r, _)| r[k].is_zero()) {
+            tighten(r[..k].to_vec(), b.clone());
+        }
+        for (p, pb) in &positive {
+            for (q, qb) in &negative {
+                let row = (0..k).map(|i| &p[i] / &p[k] - &q[i] / &q[k]).collect();
+                tighten(row, pb / &p[k] - qb / &q[k]);
+            }
+        }
+        stages.push(rows);
+        rows = next.into_iter().collect();
+        if rows
+            .iter()
+            .any(|(r, b)| r.iter().all(Zero::is_zero) && b.is_negative())
+        {
+            return Ok(None);
+        }
+    }
+    let mut point = Vec::new();
+    for stage in stages.iter().rev() {
+        let k = point.len();
+        let mut lower = BigRational::zero();
+        let mut upper: Option<BigRational> = None;
+        for (r, b) in stage {
+            let residual = b - r[..k]
+                .iter()
+                .zip(&point)
+                .map(|(a, x)| a * x)
+                .sum::<BigRational>();
+            if r[k].is_positive() {
+                let bound = residual / &r[k];
+                upper = Some(upper.map_or(bound.clone(), |u| u.min(bound)));
+            } else if r[k].is_negative() {
+                lower = lower.max(residual / &r[k]);
+            }
+        }
+        if upper.is_some_and(|u| lower > u) {
+            return Ok(None);
+        }
+        point.push(lower);
+    }
+    if !a.iter().zip(b).all(|(r, b)| {
+        r.iter()
+            .zip(&point)
+            .map(|(a, x)| a * x)
+            .sum::<BigRational>()
+            <= *b
+    }) {
+        return Err(Reason::ResourceLimit(
+            "LP certificate failed exact verification",
+        ));
+    }
+    Ok(Some(point))
+}
diff --git a/src/poly_compare/mod.rs b/src/poly_compare/mod.rs
new file mode 100644
index 000000000..1b8090618
--- /dev/null
+++ b/src/poly_compare/mod.rs
@@ -0,0 +1,1040 @@
+//! Certified V1 generic polynomial comparison relative to a fixed path batch.
+use crate::expr::{Expr, Symbol};
+use crate::parameters::{ParameterRelation, ParameterTransform, ParameterTransformError};
+use crate::polynomial::pow_rational;
+pub use crate::polynomial::{Monomial, Poly};
+use num_bigint::{BigInt, BigUint};
+use num_rational::BigRational;
+use num_traits::{One, Signed, Zero};
+use std::collections::{BTreeMap, BTreeSet, HashMap, HashSet};
+use std::sync::Arc;
+
+mod lp;
+mod render;
+
+/// Why one comparison direction is unresolved; each is a missing proof obligation.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub enum Reason {
+    NotPolynomial(String),
+    Unavailable(ParameterTransformError),
+    MissingField,
+    Validity,
+    ResourceLimit(&'static str),
+}
+
+/// One target field of a path: its certified bound plus the nominal signed composition.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub struct FieldCertificate {
+    /// Exact substitution of the registered signed formulas; audit data only.
+    pub original_signed: Option<Poly>,
+    /// The bound comparisons use, with its accuracy.
+    pub certificate: Result<(Poly, ParameterRelation), Reason>,
+}
+impl FieldCertificate {
+    pub fn new(expression: &Expr, relation: ParameterRelation) -> Self {
+        let certificate = Poly::from_expr(expression)
+            .map(|poly| (poly, relation))
+            .ok_or_else(|| Reason::NotPolynomial(expression.to_string()));
+        Self {
+            original_signed: certificate.as_ref().ok().map(|(poly, _)| poly.clone()),
+            certificate,
+        }
+    }
+    fn poly(&self) -> Result<&Poly, Reason> {
+        self.certificate
+            .as_ref()
+            .map(|(poly, _)| poly)
+            .map_err(Clone::clone)
+    }
+}
+
+/// Target fields of one path as functions of the source parameters.
+#[derive(Clone, Debug, Default, PartialEq, Eq)]
+pub struct Profile {
+    /// Full source box, including coordinates absent from every formula.
+    pub domain: BTreeSet<Symbol>,
+    pub fields: BTreeMap<String, FieldCertificate>,
+}
+impl Profile {
+    /// Profile over the variables its certificates read.
+    pub fn new(fields: BTreeMap<String, FieldCertificate>) -> Self {
+        let domain = fields
+            .values()
+            .filter_map(|f| f.poly().ok())
+            .flat_map(Poly::variables)
+            .collect();
+        Self { domain, fields }
+    }
+
+    /// Project a composed transform; composition itself is `ParameterTransform::compose`.
+    pub fn from_transform(transform: &ParameterTransform) -> Self {
+        let mut fields: BTreeMap<_, _> = transform
+            .expressions()
+            .map(|(name, expr)| {
+                let relation = transform.relation(name).expect("listed field");
+                (name.to_string(), FieldCertificate::new(expr, relation))
+            })
+            .collect();
+        for (name, error) in transform.unavailable_fields() {
+            fields.insert(
+                name.to_string(),
+                FieldCertificate {
+                    original_signed: None,
+                    certificate: Err(Reason::Unavailable(error.clone())),
+                },
+            );
+        }
+        Self::new(fields)
+    }
+
+    /// Path profile: `composed` supplies certificates; `steps` are substituted
+    /// exactly, without hulls, to recover the nominal signed formulas.
+    pub fn from_path(
+        source_parameters: &[String],
+        steps: &[ParameterTransform],
+        composed: &ParameterTransform,
+    ) -> Self {
+        let mut values: BTreeMap<Symbol, Poly> = source_parameters
+            .iter()
+            .filter_map(|name| Symbol::new(name.as_str()).ok())
+            .map(|symbol| (symbol.clone(), Poly::variable(symbol)))
+            .collect();
+        let mut profile = Self::from_transform(composed);
+        profile.domain.extend(values.keys().cloned());
+        for step in steps {
+            values = step
+                .expressions()
+                .filter_map(|(name, expr)| {
+                    let poly = Poly::from_expr(expr)?.substitute(&values)?;
+                    Some((Symbol::new(name).ok()?, poly))
+                })
+                .collect();
+        }
+        for (name, field) in &mut profile.fields {
+            field.original_signed = Symbol::new(name.as_str())
+                .ok()
+                .and_then(|symbol| values.remove(&symbol));
+        }
+        profile
+    }
+}
+
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub struct Coverage {
+    pub exponent: Monomial,
+    pub weights: Vec<(Monomial, BigRational)>,
+}
+/// Re-verified proofs of the batch-relative generic order.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub enum GenericProof {
+    Identity,
+    Zero,
+    Newton(Vec<Coverage>),
+}
+impl GenericProof {
+    pub fn verify(&self, f: &Poly, g: &Poly) -> bool {
+        match self {
+            Self::Identity => f == g,
+            Self::Zero => f.is_zero(),
+            Self::Newton(coverage) => verify_coverage(coverage, f, g),
+        }
+    }
+}
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub struct Witness {
+    pub curve: Curve,
+    pub numerator: BTreeMap<BigUint, BigRational>,
+    pub denominator: BTreeMap<BigUint, BigRational>,
+}
+type Curve = BTreeMap<Symbol, (BigUint, BigUint)>;
+fn on_curve(poly: &Poly, curve: &Curve) -> Option<BTreeMap<BigUint, BigRational>> {
+    let mut result = BTreeMap::new();
+    for (m, c) in poly.terms() {
+        let mut degree = BigUint::zero();
+        let mut coefficient = c.clone();
+        for (v, a) in m {
+            let (scale, e) = curve.get(v)?;
+            degree += a * e;
+            coefficient *= pow_rational(
+                BigRational::from_integer(BigInt::from(scale.clone())),
+                &BigInt::from(a.clone()),
+            );
+        }
+        *result.entry(degree).or_insert_with(BigRational::zero) += coefficient;
+    }
+    result.retain(|_, c| !c.is_zero());
+    Some(result)
+}
+impl Witness {
+    /// Evaluate both sides; accept only a regular-valid refutation across the batch.
+    pub fn on(curve: Curve, f: &Poly, g: &Poly, batch: &[Poly]) -> Option<Self> {
+        let w = Self {
+            numerator: on_curve(f, &curve)?,
+            denominator: on_curve(g, &curve)?,
+            curve,
+        };
+        w.verify(f, g, batch).then_some(w)
+    }
+    /// Verify exact substitutions and every original top face, before cancellation.
+    pub fn verify(&self, f: &Poly, g: &Poly, batch: &[Poly]) -> bool {
+        self.curve.values().all(|(c, _)| c >= &BigUint::from(2u8))
+            && self.curve.values().any(|(_, e)| !e.is_zero())
+            && on_curve(f, &self.curve).as_ref() == Some(&self.numerator)
+            && on_curve(g, &self.curve).as_ref() == Some(&self.denominator)
+            && batch
+                .iter()
+                .chain([f, g])
+                .filter(|p| !p.is_zero())
+                .all(|p| {
+                    // Positive coefficients cannot cancel on a curve with positive scales.
+                    p.variables().iter().all(|v| self.curve.contains_key(v))
+                        && p.terms().values().all(Signed::is_positive)
+                        || height(p, &self.curve).is_some_and(|h| {
+                            on_curve(p, &self.curve)
+                                .and_then(|terms| terms.get(&h).cloned())
+                                .is_some_and(|c| c.is_positive())
+                        })
+                })
+            && height(f, &self.curve) > height(g, &self.curve)
+    }
+}
+
+/// One generic direction: a checkable proof, a regular-valid witness, or a missing obligation.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub enum Direction {
+    Yes(GenericProof),
+    No(Witness),
+    Unknown(Reason),
+}
+impl Direction {
+    /// Kleene truth value.
+    fn holds(&self) -> Option<bool> {
+        match self {
+            Self::Yes(_) => Some(true),
+            Self::No(_) => Some(false),
+            Self::Unknown(_) => None,
+        }
+    }
+}
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Side {
+    Left,
+    Right,
+}
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Verdict {
+    Dominated {
+        worse: Side,
+    },
+    Equivalent,
+    /// Both directions refuted with verified witnesses.
+    Incomparable,
+    /// At least one direction unresolved and none refuted on both sides.
+    Unknown,
+}
+impl Verdict {
+    pub const ALL: [&'static str; 4] = ["Dominated", "Equivalent", "Incomparable", "Unknown"];
+    fn from_directions(forward: Option<bool>, reverse: Option<bool>) -> Self {
+        match (forward, reverse) {
+            (Some(true), Some(true)) => Self::Equivalent,
+            (Some(true), Some(false)) => Self::Dominated { worse: Side::Right },
+            (Some(false), Some(true)) => Self::Dominated { worse: Side::Left },
+            (Some(false), Some(false)) => Self::Incomparable,
+            _ => Self::Unknown,
+        }
+    }
+    /// Position in [`Verdict::ALL`].
+    pub fn index(self) -> usize {
+        match self {
+            Self::Dominated { .. } => 0,
+            Self::Equivalent => 1,
+            Self::Incomparable => 2,
+            Self::Unknown => 3,
+        }
+    }
+    pub fn name(self) -> &'static str {
+        Self::ALL[self.index()]
+    }
+    /// `(winner, loser)` of a dominated pair `(i, j)`; `None` for every other verdict.
+    pub fn winner_loser(self, i: usize, j: usize) -> Option<(usize, usize)> {
+        match self {
+            Self::Dominated { worse: Side::Right } => Some((i, j)),
+            Self::Dominated { worse: Side::Left } => Some((j, i)),
+            _ => None,
+        }
+    }
+}
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub struct FieldComparison {
+    pub forward: Direction,
+    pub reverse: Direction,
+}
+impl FieldComparison {
+    pub fn verdict(&self) -> Verdict {
+        Verdict::from_directions(self.forward.holds(), self.reverse.holds())
+    }
+}
+fn exponent(m: &Monomial, v: &Symbol) -> BigUint {
+    m.get(v).cloned().unwrap_or_default()
+}
+fn dominates(a: &Monomial, b: &Monomial) -> bool {
+    b.iter()
+        .all(|(v, e)| a.get(v).map_or_else(|| e.is_zero(), |power| power >= e))
+}
+impl Coverage {
+    pub fn verify(&self, denominator: &Poly) -> bool {
+        self.weights.iter().all(|(b, w)| {
+            !w.is_negative() && denominator.terms().get(b).is_some_and(|c| c.is_positive())
+        }) && self.weights.iter().map(|(_, w)| w).sum::<BigRational>() == BigRational::one()
+            && self.exponent.iter().all(|(v, e)| {
+                self.weights
+                    .iter()
+                    .map(|(b, w)| w * BigRational::from_integer(BigInt::from(exponent(b, v))))
+                    .sum::<BigRational>()
+                    >= BigRational::from_integer(BigInt::from(e.clone()))
+            })
+    }
+}
+fn verify_coverage(coverage: &[Coverage], f: &Poly, g: &Poly) -> bool {
+    coverage.len() == f.terms().values().filter(|c| c.is_positive()).count()
+        && coverage
+            .iter()
+            .map(|c| &c.exponent)
+            .collect::<BTreeSet<_>>()
+            .len()
+            == coverage.len()
+        && coverage
+            .iter()
+            .all(|c| f.terms().get(&c.exponent).is_some_and(Signed::is_positive) && c.verify(g))
+}
+/// Newton-hull LP over the positive denominator support; built once per denominator.
+struct CoverageLp<'a> {
+    support: Vec<&'a Monomial>,
+    axes: BTreeMap<Symbol, BigUint>,
+    rows: Vec<Vec<BigRational>>,
+}
+impl<'a> CoverageLp<'a> {
+    fn new(hull: &'a Poly, vars: &[Symbol]) -> Self {
+        let support: Vec<_> = hull.terms().keys().collect();
+        if support.len() <= 1 {
+            return Self {
+                support,
+                axes: BTreeMap::new(),
+                rows: Vec::new(),
+            };
+        }
+        let mut rows: Vec<Vec<_>> = vars
+            .iter()
+            .map(|v| {
+                support
+                    .iter()
+                    .map(|b| -BigRational::from_integer(BigInt::from(exponent(b, v))))
+                    .collect()
+            })
+            .collect();
+        rows.push(vec![BigRational::one(); support.len()]);
+        rows.push(vec![-BigRational::one(); support.len()]);
+        let axes = axis_support(support.iter().copied());
+        Self {
+            support,
+            axes,
+            rows,
+        }
+    }
+    fn cover(&self, a: &Monomial, vars: &[Symbol]) -> Result<Option<Coverage>, Reason> {
+        if let Some(dominator) = self.support.iter().find(|b| dominates(b, a)) {
+            return Ok(Some(Coverage {
+                exponent: a.clone(),
+                weights: vec![((*dominator).clone(), BigRational::one())],
+            }));
+        }
+        // A singleton convex hull contains no other convex combinations.
+        if self.support.len() <= 1 {
+            return Ok(None);
+        }
+        if let Some(coverage) = axis_coverage(a, &self.axes) {
+            return Ok(Some(coverage));
+        }
+        let mut rhs: Vec<_> = vars
+            .iter()
+            .map(|v| -BigRational::from_integer(BigInt::from(exponent(a, v))))
+            .collect();
+        rhs.extend([BigRational::one(), -BigRational::one()]);
+        Ok(lp::feasible(&self.rows, &rhs)?.map(|weights| Coverage {
+            exponent: a.clone(),
+            weights: self
+                .support
+                .iter()
+                .zip(weights)
+                .filter(|(_, w)| !w.is_zero())
+                .map(|(b, w)| ((*b).clone(), w))
+                .collect(),
+        }))
+    }
+}
+/// A curve along which `x^a` outgrows every monomial of `lower`.
+fn separating_curve(vars: &[Symbol], a: &Monomial, lower: &Poly) -> Result<Option<Curve>, Reason> {
+    let direction = if lower.is_zero() {
+        Some(vec![BigRational::one(); vars.len()])
+    } else {
+        let rows: Vec<_> = lower
+            .terms()
+            .keys()
+            .map(|b| {
+                vars.iter()
+                    .map(|v| {
+                        BigRational::from_integer(
+                            BigInt::from(exponent(b, v)) - BigInt::from(exponent(a, v)),
+                        )
+                    })
+                    .collect()
+            })
+            .collect();
+        lp::feasible(&rows, &vec![-BigRational::one(); lower.terms().len()])?
+    };
+    Ok(direction.map(|direction| {
+        let denominator: BigInt = direction.iter().map(|e| e.denom()).product();
+        vars.iter()
+            .zip(direction)
+            .map(|(v, e)| {
+                let e = (e * BigRational::from_integer(denominator.clone())).to_integer();
+                (v.clone(), (BigUint::from(2u8), e.magnitude().clone()))
+            })
+            .collect()
+    }))
+}
+
+/// Facts about one field shared by both directions of a comparison.
+struct Prepared<'a> {
+    poly: &'a Poly,
+    /// Positive part: an upper bound for the numerator, the Newton support for the denominator.
+    hull: Arc<Poly>,
+    support: Arc<Poly>,
+}
+
+fn axis_support<'a>(support: impl IntoIterator<Item = &'a Monomial>) -> BTreeMap<Symbol, BigUint> {
+    let mut axes = BTreeMap::new();
+    for m in support.into_iter().filter(|m| m.len() == 1) {
+        let (v, exponent) = m.first_key_value().expect("one variable");
+        axes.entry(v.clone())
+            .and_modify(|power: &mut BigUint| *power = (&*power).max(exponent).clone())
+            .or_insert_with(|| exponent.clone());
+    }
+    axes
+}
+
+fn axis_coverage(a: &Monomial, axes: &BTreeMap<Symbol, BigUint>) -> Option<Coverage> {
+    let (first, _) = axes.first_key_value()?;
+    let mut weights = BTreeMap::new();
+    let mut total = BigRational::zero();
+    for (v, e) in a {
+        // Coordinate e_i is covered by weight e_i/axis_i on its axis vertex.
+        let weight = BigRational::new(e.clone().into(), axes.get(v)?.clone().into());
+        total += &weight;
+        weights.insert(v, weight);
+    }
+    if total > BigRational::one() {
+        return None;
+    }
+    *weights.entry(first).or_default() += BigRational::one() - total;
+    Some(Coverage {
+        exponent: a.clone(),
+        weights: weights
+            .into_iter()
+            .filter(|(_, w)| !w.is_zero())
+            .map(|(v, w)| (Monomial::from([(v.clone(), axes[v].clone())]), w))
+            .collect(),
+    })
+}
+
+fn upper_support(hull: &Poly) -> Poly {
+    let axes = axis_support(hull.terms().keys());
+    let mut terms: Vec<_> = hull
+        .terms()
+        .iter()
+        .filter(|(m, _)| {
+            (m.len() == 1 && m.iter().all(|(v, e)| axes.get(v) == Some(e)))
+                || axis_coverage(m, &axes).is_none()
+        })
+        .map(|(m, c)| (m.values().sum::<BigUint>(), m, c))
+        .collect();
+    terms.sort_by(|a, b| b.0.cmp(&a.0));
+    let mut maximal = Vec::new();
+    for (_, monomial, coefficient) in terms {
+        // Descending degree means a later monomial cannot dominate an earlier one.
+        if !maximal.iter().any(|(m, _)| dominates(m, monomial)) {
+            maximal.push((monomial.clone(), coefficient.clone()));
+        }
+    }
+    Poly::from_terms(maximal)
+}
+fn monomial_degree(m: &Monomial, curve: &Curve) -> Option<BigUint> {
+    m.iter()
+        .try_fold(BigUint::zero(), |d, (v, a)| Some(d + a * &curve.get(v)?.1))
+}
+fn height(p: &Poly, curve: &Curve) -> Option<BigUint> {
+    p.terms()
+        .keys()
+        .map(|m| monomial_degree(m, curve))
+        .collect::<Option<Vec<_>>>()?
+        .into_iter()
+        .max()
+}
+
+fn refute(base: &Curve, f: &Poly, g: &Poly, batch: &mut ComparisonBatch) -> Option<Witness> {
+    let numerator = batch.evaluate_curve(f, base)?;
+    let denominator = batch.evaluate_curve(g, base)?;
+    // Support heights depend only on exponents: changing scales cannot fix a missing gap.
+    if numerator.height <= denominator.height {
+        return None;
+    }
+    if batch.regular_curve(base) {
+        return Some(Witness {
+            curve: base.clone(),
+            numerator: numerator.terms.clone(),
+            denominator: denominator.terms.clone(),
+        });
+    }
+    for scale in [3u8, 4] {
+        for coordinate in std::iter::once(None).chain(base.keys().map(Some)) {
+            let mut curve = base.clone();
+            for (v, (c, _)) in &mut curve {
+                if coordinate.is_none_or(|coordinate| coordinate == v) {
+                    *c = scale.into();
+                }
+            }
+            let numerator = batch.evaluate_curve(f, &curve)?;
+            let denominator = batch.evaluate_curve(g, &curve)?;
+            if batch.regular_curve(&curve) {
+                return Some(Witness {
+                    curve,
+                    numerator: numerator.terms.clone(),
+                    denominator: denominator.terms.clone(),
+                });
+            }
+        }
+    }
+    None
+}
+
+fn cell_curves(vars: &[Symbol], batch: &[Arc<Poly>]) -> Vec<Curve> {
+    let curve = |exponents: Vec<BigUint>| {
+        vars.iter()
+            .cloned()
+            .zip(exponents)
+            .map(|(v, e)| (v, (2u8.into(), e)))
+            .collect::<Curve>()
+    };
+    let mut curves = vec![curve(vec![BigUint::one(); vars.len()])];
+    curves.extend((0..vars.len()).map(|i| {
+        curve(
+            (0..vars.len())
+                .map(|j| BigUint::from(u8::from(i == j)))
+                .collect(),
+        )
+    }));
+    // shortcut: inspect at most 128 support pairs and keep 32 exposed tie directions; exhaustive fans are deferred.
+    let mut inspected = 0;
+    let mut ties = 0;
+    for p in batch {
+        let support: Vec<_> = p.terms().keys().collect();
+        for (i, a) in support.iter().enumerate() {
+            for b in &support[i + 1..] {
+                inspected += 1;
+                if inspected > 128 {
+                    return curves;
+                }
+                for (i, v) in vars.iter().enumerate() {
+                    let dv = BigInt::from(exponent(a, v)) - BigInt::from(exponent(b, v));
+                    for (j, w) in vars.iter().enumerate().skip(i + 1) {
+                        let dw = BigInt::from(exponent(a, w)) - BigInt::from(exponent(b, w));
+                        if !(&dv * &dw).is_negative() {
+                            continue;
+                        }
+                        let mut exponents = vec![BigUint::zero(); vars.len()];
+                        exponents[i] = dw.magnitude().clone();
+                        exponents[j] = dv.magnitude().clone();
+                        let c = curve(exponents);
+                        let h = height(p, &c);
+                        if h == monomial_degree(a, &c)
+                            && h == monomial_degree(b, &c)
+                            && !curves.contains(&c)
+                        {
+                            curves.push(c);
+                            ties += 1;
+                            if ties == 32 {
+                                return curves;
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+    curves
+}
+
+struct ComparisonBatch {
+    polynomials: Vec<Arc<Poly>>,
+    indices: HashMap<Arc<Poly>, usize>,
+    hulls: Vec<Arc<Poly>>,
+    supports: Vec<Arc<Poly>>,
+    domain: BTreeSet<Symbol>,
+    signed: Vec<usize>,
+    evaluations: HashMap<usize, HashMap<Curve, Option<Arc<CurveEvaluation>>>>,
+    regular: HashMap<Curve, bool>,
+    curves: HashMap<Vec<Symbol>, Arc<Vec<Curve>>>,
+}
+struct CurveEvaluation {
+    terms: BTreeMap<BigUint, BigRational>,
+    height: Option<BigUint>,
+    regular: bool,
+}
+impl ComparisonBatch {
+    fn new(polynomials: Vec<Poly>) -> Self {
+        let polynomials: Vec<_> = std::iter::once(Poly::zero())
+            .chain(polynomials)
+            .map(Arc::new)
+            .collect();
+        let indices = polynomials
+            .iter()
+            .enumerate()
+            .map(|(i, p)| (p.clone(), i))
+            .collect();
+        let domain = polynomials.iter().flat_map(|p| p.variables()).collect();
+        let hulls: Vec<_> = polynomials
+            .iter()
+            .map(|p| {
+                if p.terms().values().all(Signed::is_positive) {
+                    p.clone()
+                } else {
+                    Arc::new(p.positive_hull())
+                }
+            })
+            .collect();
+        let supports = hulls.iter().map(|h| Arc::new(upper_support(h))).collect();
+        let signed = polynomials
+            .iter()
+            .enumerate()
+            .filter_map(|(i, p)| p.terms().values().any(Signed::is_negative).then_some(i))
+            .collect();
+        Self {
+            polynomials,
+            indices,
+            hulls,
+            supports,
+            domain,
+            signed,
+            evaluations: HashMap::new(),
+            regular: HashMap::new(),
+            curves: HashMap::new(),
+        }
+    }
+
+    fn prepare<'a>(&self, poly: &'a Poly) -> Prepared<'a> {
+        let i = self.indices[poly];
+        Prepared {
+            poly,
+            hull: self.hulls[i].clone(),
+            support: self.supports[i].clone(),
+        }
+    }
+
+    fn evaluate_index(&mut self, index: usize, curve: &Curve) -> Option<Arc<CurveEvaluation>> {
+        let evaluations = self.evaluations.entry(index).or_default();
+        if let Some(evaluation) = evaluations.get(curve) {
+            return evaluation.clone();
+        }
+        let poly = &self.polynomials[index];
+        let evaluation = on_curve(poly, curve).map(|terms| {
+            let height = height(poly, curve);
+            let regular = height
+                .as_ref()
+                .and_then(|h| terms.get(h))
+                .is_some_and(Signed::is_positive);
+            Arc::new(CurveEvaluation {
+                terms,
+                height,
+                regular,
+            })
+        });
+        evaluations.insert(curve.clone(), evaluation.clone());
+        evaluation
+    }
+
+    fn evaluate_curve(&mut self, poly: &Poly, curve: &Curve) -> Option<Arc<CurveEvaluation>> {
+        let index = *self.indices.get(poly)?;
+        self.evaluate_index(index, curve)
+    }
+
+    fn regular_curve(&mut self, curve: &Curve) -> bool {
+        if let Some(&regular) = self.regular.get(curve) {
+            return regular;
+        }
+        let mut regular = curve
+            .values()
+            .all(|(scale, _)| scale >= &BigUint::from(2u8))
+            && curve.values().any(|(_, exponent)| !exponent.is_zero())
+            && self.domain.iter().all(|v| curve.contains_key(v));
+        for i in 0..self.signed.len() {
+            if !regular {
+                break;
+            }
+            regular = self
+                .evaluate_index(self.signed[i], curve)
+                .is_some_and(|e| e.regular);
+        }
+        self.regular.insert(curve.clone(), regular);
+        regular
+    }
+}
+
+fn direction(
+    f: &Prepared,
+    g: &Prepared,
+    vars: &[Symbol],
+    batch: &mut ComparisonBatch,
+) -> Direction {
+    let immediate = if f.poly == g.poly {
+        Some(GenericProof::Identity)
+    } else if f.poly.is_zero() {
+        Some(GenericProof::Zero)
+    } else {
+        None
+    };
+    if let Some(proof) = immediate {
+        if proof.verify(f.poly, g.poly) {
+            return Direction::Yes(proof);
+        }
+    }
+    let lp = CoverageLp::new(&g.support, vars);
+    let coverage: Result<Option<Vec<_>>, _> =
+        f.hull.terms().keys().map(|a| lp.cover(a, vars)).collect();
+    let mut reason = match coverage {
+        Ok(Some(coverage)) => {
+            let proof = GenericProof::Newton(coverage);
+            if proof.verify(f.poly, g.poly) {
+                return Direction::Yes(proof);
+            }
+            Reason::Validity
+        }
+        Ok(None) => Reason::Validity,
+        Err(reason) => reason,
+    };
+    let curves = batch
+        .curves
+        .entry(vars.to_vec())
+        .or_insert_with(|| Arc::new(cell_curves(vars, &batch.polynomials)))
+        .clone();
+    for curve in curves.iter() {
+        if let Some(w) = refute(curve, f.poly, g.poly, batch) {
+            return Direction::No(w);
+        }
+    }
+    for a in f.support.terms().keys() {
+        match separating_curve(vars, a, &g.support) {
+            Ok(Some(curve)) => {
+                // Curves include the full batch domain; positive polynomials cannot cancel.
+                if let Some(w) = refute(&curve, f.poly, g.poly, batch) {
+                    return Direction::No(w);
+                }
+            }
+            Err(error) => reason = error,
+            Ok(None) => {}
+        }
+    }
+    Direction::Unknown(reason)
+}
+/// Compare chosen certificates in the generic order, with a batch of these two fields, over `domain`
+/// plus every variable either side reads. Unused coordinates matter:
+/// bounded-variable slices still escape to infinity.
+pub fn compare(
+    f: &FieldCertificate,
+    g: &FieldCertificate,
+    domain: &BTreeSet<Symbol>,
+) -> FieldComparison {
+    let batch: Vec<_> = [f, g]
+        .iter()
+        .filter_map(|f| f.poly().ok())
+        .filter(|p| !p.is_zero())
+        .cloned()
+        .collect();
+    compare_in_batch(f, g, domain, &mut ComparisonBatch::new(batch))
+}
+fn compare_in_batch(
+    f: &FieldCertificate,
+    g: &FieldCertificate,
+    domain: &BTreeSet<Symbol>,
+    batch: &mut ComparisonBatch,
+) -> FieldComparison {
+    let both = |reason: Reason| FieldComparison {
+        forward: Direction::Unknown(reason.clone()),
+        reverse: Direction::Unknown(reason),
+    };
+    let (fp, gp) = match (f.poly(), g.poly()) {
+        (Ok(fp), Ok(gp)) => (fp, gp),
+        (Err(reason), _) | (_, Err(reason)) => return both(reason),
+    };
+    let mut ambient = domain.clone();
+    ambient.extend(batch.domain.iter().cloned());
+    ambient.extend(fp.variables());
+    ambient.extend(gp.variables());
+    let vars: Vec<_> = ambient.into_iter().collect();
+    let [fs, gs] = [fp, gp].map(|poly| batch.prepare(poly));
+    FieldComparison {
+        forward: direction(&fs, &gs, &vars, batch),
+        reverse: direction(&gs, &fs, &vars, batch),
+    }
+}
+
+/// Field-wise comparison of two paths under the product order.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub struct ProfileComparison {
+    pub fields: BTreeMap<String, FieldComparison>,
+    pub verdict: Verdict,
+}
+pub fn compare_profiles(f: &Profile, g: &Profile) -> ProfileComparison {
+    compare_profiles_in_batch(f, g, &mut ComparisonBatch::new(batch_certificates([f, g])))
+}
+fn batch_certificates<'a>(profiles: impl IntoIterator<Item = &'a Profile>) -> Vec<Poly> {
+    let mut batch = Vec::new();
+    let mut seen = HashSet::new();
+    for p in profiles
+        .into_iter()
+        .flat_map(|p| p.fields.values())
+        .filter_map(|f| f.poly().ok())
+    {
+        if !p.is_zero() && seen.insert(p) {
+            batch.push(p.clone());
+        }
+    }
+    batch
+}
+fn compare_profiles_in_batch(
+    f: &Profile,
+    g: &Profile,
+    batch: &mut ComparisonBatch,
+) -> ProfileComparison {
+    let missing = FieldCertificate {
+        original_signed: None,
+        certificate: Err(Reason::MissingField),
+    };
+    let domain: BTreeSet<_> = f.domain.union(&g.domain).cloned().collect();
+    let fields: BTreeMap<_, _> = f
+        .fields
+        .keys()
+        .chain(g.fields.keys())
+        .collect::<BTreeSet<_>>()
+        .into_iter()
+        .map(|name| {
+            let comparison = compare_in_batch(
+                f.fields.get(name).unwrap_or(&missing),
+                g.fields.get(name).unwrap_or(&missing),
+                &domain,
+                batch,
+            );
+            (name.clone(), comparison)
+        })
+        .collect();
+    // Kleene conjunction over fields: any refutation wins, otherwise any unknown.
+    let all = |pick: fn(&FieldComparison) -> Option<bool>| {
+        let mut result = Some(true);
+        for c in fields.values() {
+            match pick(c) {
+                Some(false) => return Some(false),
+                None => result = None,
+                Some(true) => {}
+            }
+        }
+        result
+    };
+    let verdict = Verdict::from_directions(all(|c| c.forward.holds()), all(|c| c.reverse.holds()));
+    ProfileComparison { fields, verdict }
+}
+
+/// All pairwise comparisons of a path batch and its candidate front.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub struct PathComparison {
+    /// `(i, j, comparison)` for every `i < j`, in order.
+    pub pairs: Vec<(usize, usize, ProfileComparison)>,
+    /// Paths that no other path strictly dominates. Final-front filtering only:
+    /// prefixes are never pruned, and equivalent paths are all kept.
+    pub front: Vec<usize>,
+}
+impl PathComparison {
+    /// Pair counts per verdict, ordered as [`Verdict::ALL`].
+    pub fn counts(&self) -> [usize; 4] {
+        let mut counts = [0; 4];
+        for (_, _, c) in &self.pairs {
+            counts[c.verdict.index()] += 1;
+        }
+        counts
+    }
+}
+/// All pair counts and candidate paths, without allocating pairwise proof records.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub struct ComparisonSummary {
+    pub counts: [usize; 4],
+    pub front: Vec<usize>,
+}
+
+pub fn compare_summary(profiles: &[Profile]) -> ComparisonSummary {
+    // Keep every certificate in the validity batch, including grouped signed polynomials.
+    let mut batch = ComparisonBatch::new(batch_certificates(profiles));
+    let mut groups = HashMap::new();
+    let mut representatives = Vec::new();
+    let mut sizes = Vec::new();
+    let mut classes = Vec::with_capacity(profiles.len());
+    for profile in profiles {
+        // On a valid family, height equals positive-support height. Coefficients,
+        // accuracy tags and dominated support points do not change that height.
+        let key = (
+            &profile.domain,
+            profile
+                .fields
+                .iter()
+                .map(|(name, field)| {
+                    (
+                        name,
+                        field.poly().ok().map(|poly| {
+                            batch
+                                .prepare(poly)
+                                .support
+                                .terms()
+                                .keys()
+                                .cloned()
+                                .collect::<Vec<_>>()
+                        }),
+                    )
+                })
+                .collect::<Vec<_>>(),
+        );
+        let class = *groups.entry(key).or_insert_with(|| {
+            representatives.push(Profile {
+                domain: profile.domain.clone(),
+                fields: profile
+                    .fields
+                    .iter()
+                    .map(|(name, field)| {
+                        let certificate = field
+                            .certificate
+                            .as_ref()
+                            .map(|(poly, relation)| {
+                                (
+                                    Poly::from_terms(
+                                        batch
+                                            .prepare(poly)
+                                            .support
+                                            .terms()
+                                            .keys()
+                                            .map(|m| (m.clone(), BigRational::one())),
+                                    ),
+                                    *relation,
+                                )
+                            })
+                            .map_err(Clone::clone);
+                        (
+                            name.clone(),
+                            FieldCertificate {
+                                original_signed: None,
+                                certificate,
+                            },
+                        )
+                    })
+                    .collect(),
+            });
+            sizes.push(0usize);
+            representatives.len() - 1
+        });
+        sizes[class] += 1;
+        classes.push(class);
+    }
+    // Positive support projections have the same height on every valid original
+    // family. Adding them cannot restrict the original batch's valid families.
+    for poly in batch_certificates(&representatives) {
+        if !batch.indices.contains_key(&poly) {
+            let hull = Arc::new(poly);
+            batch.indices.insert(hull.clone(), batch.polynomials.len());
+            batch.supports.push(hull.clone());
+            batch.hulls.push(hull.clone());
+            batch.polynomials.push(hull);
+        }
+    }
+    let mut counts = [0; 4];
+    let mut dominated = vec![false; representatives.len()];
+    for (i, left) in representatives.iter().enumerate() {
+        for (j, right) in representatives.iter().enumerate().skip(i) {
+            let multiplicity = if i == j {
+                sizes[i] * (sizes[i] - 1) / 2
+            } else {
+                sizes[i] * sizes[j]
+            };
+            if multiplicity == 0 {
+                continue;
+            }
+            let verdict = compare_profiles_in_batch(left, right, &mut batch).verdict;
+            counts[verdict.index()] += multiplicity;
+            if let Verdict::Dominated { worse } = verdict {
+                dominated[if worse == Side::Left { i } else { j }] = true;
+            }
+        }
+    }
+    ComparisonSummary {
+        counts,
+        front: classes
+            .iter()
+            .enumerate()
+            .filter_map(|(i, &class)| (!dominated[class]).then_some(i))
+            .collect(),
+    }
+}
+
+pub fn compare_all(profiles: &[Profile]) -> PathComparison {
+    let mut batch = ComparisonBatch::new(batch_certificates(profiles));
+    // Identical profiles share one comparison result.
+    let mut representatives: Vec<usize> = Vec::new();
+    let class: Vec<usize> = profiles
+        .iter()
+        .enumerate()
+        .map(|(i, p)| {
+            representatives
+                .iter()
+                .position(|&r| profiles[r] == *p)
+                .unwrap_or_else(|| {
+                    representatives.push(i);
+                    representatives.len() - 1
+                })
+        })
+        .collect();
+    let mut cache = HashMap::new();
+    let mut dominated = BTreeSet::new();
+    let mut pairs = Vec::new();
+    for i in 0..profiles.len() {
+        for j in i + 1..profiles.len() {
+            let comparison = cache
+                .entry((class[i], class[j]))
+                .or_insert_with(|| {
+                    compare_profiles_in_batch(
+                        &profiles[representatives[class[i]]],
+                        &profiles[representatives[class[j]]],
+                        &mut batch,
+                    )
+                })
+                .clone();
+            if let Verdict::Dominated { worse } = comparison.verdict {
+                dominated.insert(if worse == Side::Left { i } else { j });
+            }
+            pairs.push((i, j, comparison));
+        }
+    }
+    PathComparison {
+        pairs,
+        front: (0..profiles.len())
+            .filter(|i| !dominated.contains(i))
+            .collect(),
+    }
+}
+
+#[cfg(test)]
+#[path = "../unit_tests/poly_compare.rs"]
+mod tests;
diff --git a/src/poly_compare/render.rs b/src/poly_compare/render.rs
new file mode 100644
index 000000000..cdec90e6d
--- /dev/null
+++ b/src/poly_compare/render.rs
@@ -0,0 +1,201 @@
+//! Human-readable certificates and the version-5 exact JSON proof schema.
+use super::*;
+use serde::{Serialize, Serializer};
+use serde_json::{json, Value};
+use std::fmt;
+
+fn monomial(m: &Monomial) -> String {
+    Poly::from_terms([(m.clone(), BigRational::one())])
+        .to_expr()
+        .to_string()
+}
+fn powers(m: &Monomial) -> Value {
+    json!(m
+        .iter()
+        .map(|(v, e)| (v.to_string(), e.to_string()))
+        .collect::<BTreeMap<_, _>>())
+}
+fn domain(d: &BTreeSet<Symbol>) -> Vec<String> {
+    d.iter().map(ToString::to_string).collect()
+}
+fn power_term(coefficient: impl fmt::Display, degree: &BigUint) -> String {
+    if degree.is_zero() {
+        coefficient.to_string()
+    } else if degree.is_one() {
+        format!("{coefficient}·t")
+    } else {
+        format!("{coefficient}·t^{degree}")
+    }
+}
+fn leading(p: &BTreeMap<BigUint, BigRational>) -> String {
+    p.last_key_value()
+        .map(|(e, c)| power_term(c, e))
+        .unwrap_or_else(|| "0".into())
+}
+fn univariate(p: &BTreeMap<BigUint, BigRational>) -> Value {
+    json!(p
+        .iter()
+        .map(|(e, c)| json!({"exponent":e.to_string(), "coefficient":c.to_string()}))
+        .collect::<Vec<_>>())
+}
+
+impl fmt::Display for Reason {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        match self {
+            Self::NotPolynomial(s) => write!(f, "not polynomial: {s}"),
+            Self::Unavailable(e) => write!(f, "unavailable: {e}"),
+            Self::MissingField => write!(f, "field missing on one path"),
+            Self::Validity => write!(f, "Newton coverage fails; no regular witness found positive for every batch certificate"),
+            Self::ResourceLimit(s) => write!(f, "resource limit: {s}"),
+        }
+    }
+}
+/// `= formula`, `<= formula`, or `unavailable: reason`.
+impl fmt::Display for FieldCertificate {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        match &self.certificate {
+            Ok((poly, ParameterRelation::Exact)) => write!(f, "= {}", poly.to_expr()),
+            Ok((poly, ParameterRelation::UpperBound)) => {
+                write!(f, "<= {}", poly.to_expr())
+            }
+            Err(reason) => write!(f, "unavailable: {reason}"),
+        }
+    }
+}
+impl fmt::Display for Verdict {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(self.name())
+    }
+}
+impl fmt::Display for Coverage {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        let terms = self
+            .weights
+            .iter()
+            .map(|(m, w)| format!("{w}·({})", monomial(m)))
+            .collect::<Vec<_>>();
+        write!(f, "{} ≤ {}", monomial(&self.exponent), terms.join(" + "))
+    }
+}
+impl fmt::Display for GenericProof {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        match self {
+            Self::Identity => write!(f, "f ≡ g after expansion"),
+            Self::Zero => write!(f, "f ≡ 0 after expansion"),
+            Self::Newton(coverage) => {
+                write!(f, "every monomial of f⁺ lies in the Newton hull of g⁺")?;
+                for c in coverage {
+                    write!(f, "\n  {c}")?;
+                }
+                Ok(())
+            }
+        }
+    }
+}
+impl fmt::Display for Witness {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        let curve = self
+            .curve
+            .iter()
+            .map(|(v, (c, e))| format!("{v} = {}", power_term(c, e)))
+            .collect::<Vec<_>>();
+        write!(
+            f,
+            "{}; f ~ {}, ",
+            curve.join(", "),
+            leading(&self.numerator)
+        )?;
+        if self.denominator.is_empty() {
+            write!(f, "g ≡ 0; positive f cannot be bounded by g")
+        } else {
+            write!(f, "g ~ {}; f/g → ∞", leading(&self.denominator))
+        }
+    }
+}
+impl fmt::Display for Direction {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        match self {
+            Self::Yes(p) => write!(f, "Yes: {p}"),
+            Self::No(w) => write!(f, "No (regular and positive across the batch): {w}"),
+            Self::Unknown(reason) => write!(f, "Unknown: missing obligation: {reason}"),
+        }
+    }
+}
+
+// Exact numbers are decimal strings (rationals use reduced p/q), independent of JSON numeric precision.
+macro_rules! serialize_view {
+    ($ty:ty, $value:ident, $body:expr) => {
+        impl Serialize for $ty {
+            fn serialize<S: Serializer>(&self, serializer: S) -> Result<S::Ok, S::Error> {
+                let $value = self;
+                let view: Value = $body;
+                view.serialize(serializer)
+            }
+        }
+    };
+}
+serialize_view!(
+    Reason,
+    r,
+    match r {
+        Reason::NotPolynomial(s) => json!({"kind":"not_polynomial", "detail":s}),
+        Reason::Unavailable(e) => json!({"kind":"unavailable", "detail":e.to_string()}),
+        Reason::MissingField => json!({"kind":"missing_field"}),
+        Reason::Validity => json!({"kind":"validity"}),
+        Reason::ResourceLimit(s) => json!({"kind":"resource_limit", "detail":s}),
+    }
+);
+serialize_view!(
+    FieldCertificate,
+    c,
+    json!({
+        "original_signed": c.original_signed.as_ref().map(|p| p.to_expr().to_string()),
+        "certificate": c.certificate.as_ref().ok().map(|(p, _)| p.to_expr().to_string()),
+        "accuracy": match &c.certificate {
+            Ok((_, relation)) => json!({"kind": relation}),
+            Err(reason) => json!({"kind":"unavailable", "reason":reason}),
+        },
+    })
+);
+serialize_view!(
+    Profile,
+    p,
+    json!({"source_coordinates":domain(&p.domain), "fields":p.fields})
+);
+serialize_view!(Verdict, v, json!(v.name()));
+serialize_view!(
+    FieldComparison,
+    c,
+    json!({"forward":c.forward, "reverse":c.reverse})
+);
+serialize_view!(
+    Coverage,
+    c,
+    json!({"exponent":powers(&c.exponent), "weights":c.weights.iter().map(|(m,w)| json!({"exponent":powers(m), "weight":w.to_string()})).collect::<Vec<_>>()})
+);
+serialize_view!(
+    GenericProof,
+    p,
+    match p {
+        GenericProof::Identity => json!({"kind":"identity"}),
+        GenericProof::Zero => json!({"kind":"zero"}),
+        GenericProof::Newton(coverage) => json!({"kind":"newton", "coverage":coverage}),
+    }
+);
+serialize_view!(
+    Witness,
+    w,
+    json!({"kind":"witness", "curve":w.curve.iter().map(|(v,(c,e))| (v.to_string(),json!({"scale":c.to_string(),"exponent":e.to_string()}))).collect::<BTreeMap<_,_>>(),"numerator":univariate(&w.numerator),"denominator":univariate(&w.denominator)})
+);
+serialize_view!(
+    Direction,
+    d,
+    match d {
+        Direction::Yes(p) => json!({"status":"Yes","certificate":p}),
+        Direction::No(w) => json!({"status":"No","certificate":w}),
+        Direction::Unknown(reason) => json!({"status":"Unknown","missing_obligation":reason}),
+    }
+);
+#[cfg(test)]
+#[path = "../unit_tests/poly_compare_render.rs"]
+mod tests;
diff --git a/src/polynomial.rs b/src/polynomial.rs
new file mode 100644
index 000000000..067e783bf
--- /dev/null
+++ b/src/polynomial.rs
@@ -0,0 +1,298 @@
+//! Exact sparse multivariate polynomials with rational coefficients.
+//!
+//! Shared by parameter-transform composition and certified polynomial comparison.
+use crate::expr::{Expr, ExprNode, Symbol};
+use num_bigint::{BigInt, BigUint};
+use num_rational::BigRational;
+use num_traits::{One, Signed, Zero};
+use std::collections::{BTreeMap, BTreeSet, HashMap};
+
+/// Variable exponents of one monomial; absent variables have exponent zero.
+pub type Monomial = BTreeMap<Symbol, BigUint>;
+
+/// Canonical polynomial: sorted support, no zero coefficients.
+#[derive(Clone, Debug, Default, PartialEq, Eq, Hash)]
+pub struct Poly(BTreeMap<Monomial, BigRational>);
+
+impl Poly {
+    /// Expand an expression; `None` when it is not a polynomial.
+    pub fn from_expr(expression: &Expr) -> Option<Self> {
+        Some(match expression.node() {
+            ExprNode::Const(value) => Self::constant(value.clone()),
+            ExprNode::Var(variable) => Self::variable(variable.clone()),
+            ExprNode::Add(values) => {
+                let mut terms = Vec::new();
+                for value in values {
+                    terms.extend(Self::from_expr(value)?.0);
+                }
+                Self::from_terms(terms)
+            }
+            ExprNode::Mul(values) => values.iter().try_fold(Self::one(), |product, value| {
+                Some(product.mul(&Self::from_expr(value)?))
+            })?,
+            ExprNode::Pow(base, exponent) => {
+                let ExprNode::Const(exponent) = exponent.node() else {
+                    return None;
+                };
+                if !exponent.is_integer() {
+                    return None;
+                }
+                if exponent.is_negative() {
+                    let ExprNode::Const(base) = base.node() else {
+                        return None;
+                    };
+                    if base.is_zero() {
+                        return None;
+                    }
+                    return Some(Self::constant(pow_rational(
+                        base.clone(),
+                        &exponent.to_integer(),
+                    )));
+                }
+                Self::from_expr(base)?.pow(exponent.to_integer().magnitude())
+            }
+            ExprNode::Exp(_) | ExprNode::Log(_) | ExprNode::Factorial(_) => return None,
+        })
+    }
+
+    pub fn zero() -> Self {
+        Self::default()
+    }
+
+    pub fn one() -> Self {
+        Self::constant(BigRational::one())
+    }
+
+    pub fn constant(value: BigRational) -> Self {
+        Self::from_terms([(Monomial::new(), value)])
+    }
+
+    pub fn variable(variable: Symbol) -> Self {
+        Self::from_terms([(
+            Monomial::from([(variable, BigUint::one())]),
+            BigRational::one(),
+        )])
+    }
+
+    /// Combine like terms and drop zero coefficients.
+    pub fn from_terms(terms: impl IntoIterator<Item = (Monomial, BigRational)>) -> Self {
+        let mut result = BTreeMap::new();
+        for (mut monomial, coefficient) in terms {
+            monomial.retain(|_, exponent| !exponent.is_zero());
+            *result.entry(monomial).or_insert_with(BigRational::zero) += coefficient;
+        }
+        result.retain(|_, coefficient: &mut BigRational| !coefficient.is_zero());
+        Self(result)
+    }
+
+    pub fn terms(&self) -> &BTreeMap<Monomial, BigRational> {
+        &self.0
+    }
+
+    pub fn is_zero(&self) -> bool {
+        self.0.is_empty()
+    }
+
+    pub fn variables(&self) -> BTreeSet<Symbol> {
+        self.0.keys().flat_map(|m| m.keys().cloned()).collect()
+    }
+
+    pub fn add(&self, other: &Self) -> Self {
+        Self::from_terms(
+            self.0
+                .iter()
+                .chain(&other.0)
+                .map(|(m, c)| (m.clone(), c.clone())),
+        )
+    }
+
+    pub fn mul(&self, other: &Self) -> Self {
+        if self
+            .0
+            .values()
+            .chain(other.0.values())
+            .all(BigRational::is_integer)
+        {
+            if let Some(product) = self.mul_integer_dense(other) {
+                return product;
+            }
+            // Integer convolution avoids fraction reduction for every pair of terms.
+            let mut terms = HashMap::<Monomial, BigInt>::new();
+            for (left, a) in &self.0 {
+                for (right, b) in &other.0 {
+                    *terms.entry(multiply_monomials(left, right)).or_default() +=
+                        a.numer() * b.numer();
+                }
+            }
+            return Self::from_terms(
+                terms
+                    .into_iter()
+                    .map(|(m, c)| (m, BigRational::from_integer(c))),
+            );
+        }
+        Self::from_terms(self.0.iter().flat_map(|(left, a)| {
+            other
+                .0
+                .iter()
+                .map(move |(right, b)| (multiply_monomials(left, right), a * b))
+        }))
+    }
+
+    fn mul_integer_dense(&self, other: &Self) -> Option<Self> {
+        let mut axes = Vec::new();
+        let mut cells = 1usize;
+        for variable in self.variables().union(&other.variables()) {
+            let degree = |p: &Self| {
+                p.0.keys()
+                    .filter_map(|m| m.get(variable))
+                    .max()
+                    .cloned()
+                    .unwrap_or_default()
+            };
+            let radix = usize::try_from(degree(self) + degree(other))
+                .ok()?
+                .checked_add(1)?;
+            axes.push((variable.clone(), radix, cells));
+            cells = cells.checked_mul(radix)?;
+            // Bound scratch memory to 65,536 BigInts; sparse or huge exponent boxes use the map.
+            if cells > 65_536 {
+                return None;
+            }
+        }
+        if cells > self.0.len().saturating_mul(other.0.len()).saturating_mul(2) {
+            return None;
+        }
+        let [left, right] = [self, other].map(|p| {
+            p.0.iter()
+                .map(|(m, c)| {
+                    let mut index = 0;
+                    for (v, _, stride) in &axes {
+                        if let Some(exponent) = m.get(v) {
+                            index += usize::try_from(exponent).ok()? * stride;
+                        }
+                    }
+                    Some((index, c.numer()))
+                })
+                .collect::<Option<Vec<_>>>()
+        });
+        let left = left?;
+        let right = right?;
+        let mut coefficients = vec![BigInt::zero(); cells];
+        for (a, c) in left {
+            for (b, d) in &right {
+                // Mixed-radix bounds include both operands, so exponent addition has no carry.
+                coefficients[a + b] += c * *d;
+            }
+        }
+        Some(Self(
+            coefficients
+                .into_iter()
+                .enumerate()
+                .filter(|(_, c)| !c.is_zero())
+                .map(|(index, c)| {
+                    let monomial = axes
+                        .iter()
+                        .filter_map(|(v, radix, stride)| {
+                            let exponent = (index / stride) % radix;
+                            (exponent != 0).then(|| (v.clone(), BigUint::from(exponent)))
+                        })
+                        .collect();
+                    (monomial, BigRational::from_integer(c))
+                })
+                .collect(),
+        ))
+    }
+
+    pub fn pow(&self, exponent: &BigUint) -> Self {
+        let mut exponent = exponent.clone();
+        let mut base = self.clone();
+        let mut result = Self::one();
+        while !exponent.is_zero() {
+            if exponent.bit(0) {
+                result = result.mul(&base);
+            }
+            exponent >>= 1usize;
+            if !exponent.is_zero() {
+                base = base.mul(&base);
+            }
+        }
+        result
+    }
+
+    /// Drop negative terms unless `keep_negative` accepts their monomial.
+    pub fn hull(&self, keep_negative: impl Fn(&Monomial) -> bool) -> Self {
+        Self(
+            self.0
+                .iter()
+                .filter(|(m, c)| c.is_positive() || keep_negative(m))
+                .map(|(m, c)| (m.clone(), c.clone()))
+                .collect(),
+        )
+    }
+
+    /// Positive part: every negative term removed.
+    pub fn positive_hull(&self) -> Self {
+        self.hull(|_| false)
+    }
+
+    /// Exact substitution; `None` when a variable has no replacement.
+    pub fn substitute(&self, replacements: &BTreeMap<Symbol, Poly>) -> Option<Self> {
+        let mut terms = Vec::new();
+        for (monomial, coefficient) in &self.0 {
+            let term = monomial.iter().try_fold(
+                Self::constant(coefficient.clone()),
+                |term, (variable, exponent)| {
+                    Some(term.mul(&replacements.get(variable)?.pow(exponent)))
+                },
+            )?;
+            terms.extend(term.0);
+        }
+        Some(Self::from_terms(terms))
+    }
+
+    pub fn to_expr(&self) -> Expr {
+        self.0
+            .iter()
+            .map(|(m, c)| {
+                m.iter().fold(Expr::constant(c.clone()), |t, (v, e)| {
+                    t * Expr::pow(
+                        Expr::variable(v.as_str()),
+                        Expr::integer(BigInt::from(e.clone())),
+                    )
+                })
+            })
+            .sum()
+    }
+}
+
+fn multiply_monomials(left: &Monomial, right: &Monomial) -> Monomial {
+    let mut monomial = left.clone();
+    for (variable, exponent) in right {
+        *monomial.entry(variable.clone()).or_default() += exponent;
+    }
+    monomial
+}
+
+pub(crate) fn pow_rational(mut base: BigRational, exponent: &BigInt) -> BigRational {
+    let negative = exponent.is_negative();
+    let mut exponent = exponent.magnitude().clone();
+    let mut result = BigRational::one();
+    while !exponent.is_zero() {
+        if exponent.bit(0) {
+            result *= &base;
+        }
+        exponent >>= 1usize;
+        if !exponent.is_zero() {
+            base = &base * &base;
+        }
+    }
+    if negative {
+        result.recip()
+    } else {
+        result
+    }
+}
+
+#[cfg(test)]
+#[path = "unit_tests/polynomial.rs"]
+mod tests;
diff --git a/src/problem_parameters.rs b/src/problem_parameters.rs
new file mode 100644
index 000000000..8e97d5b86
--- /dev/null
+++ b/src/problem_parameters.rs
@@ -0,0 +1,90 @@
+//! Canonical problem-instance parameters, shared with the browser.
+use serde::{Deserialize, Serialize};
+use std::fmt;
+
+/// Canonical named parameters for one concrete problem instance.
+#[derive(Debug, Clone, Default, PartialEq, Eq, Serialize, Deserialize)]
+pub struct ProblemParameters {
+    /// Named parameters in canonical declaration order.
+    #[serde(deserialize_with = "deserialize_parameter_components")]
+    pub(crate) components: Vec<(String, u64)>,
+}
+
+impl ProblemParameters {
+    /// Create problem parameters in canonical declaration order.
+    ///
+    /// # Panics
+    /// Panics if a parameter name occurs more than once.
+    pub fn new(components: Vec<(&str, u64)>) -> Self {
+        Self::from_owned(
+            components
+                .into_iter()
+                .map(|(name, value)| (name.to_string(), value))
+                .collect(),
+        )
+    }
+
+    /// Create problem parameters from owned names.
+    ///
+    /// # Panics
+    /// Panics if a parameter name occurs more than once.
+    pub fn from_owned(components: Vec<(String, u64)>) -> Self {
+        if let Some(name) = duplicate_parameter_name(&components) {
+            panic!("duplicate problem parameter `{name}`");
+        }
+        Self { components }
+    }
+
+    /// Iterate over parameters in canonical declaration order.
+    pub fn iter(&self) -> impl Iterator<Item = (&str, u64)> {
+        self.components
+            .iter()
+            .map(|(name, value)| (name.as_str(), *value))
+    }
+
+    /// Get a parameter by name.
+    pub fn get(&self, name: &str) -> Option<u64> {
+        self.components
+            .iter()
+            .find(|(k, _)| k == name)
+            .map(|(_, v)| *v)
+    }
+}
+
+fn duplicate_parameter_name(components: &[(String, u64)]) -> Option<&str> {
+    components
+        .iter()
+        .enumerate()
+        .find_map(|(index, (name, _))| {
+            components[..index]
+                .iter()
+                .any(|(previous, _)| previous == name)
+                .then_some(name.as_str())
+        })
+}
+
+fn deserialize_parameter_components<'de, D>(deserializer: D) -> Result<Vec<(String, u64)>, D::Error>
+where
+    D: serde::Deserializer<'de>,
+{
+    let components = Vec::<(String, u64)>::deserialize(deserializer)?;
+    if let Some(name) = duplicate_parameter_name(&components) {
+        return Err(serde::de::Error::custom(format!(
+            "duplicate problem parameter `{name}`"
+        )));
+    }
+    Ok(components)
+}
+
+impl fmt::Display for ProblemParameters {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        write!(f, "ProblemParameters{{")?;
+        for (i, (name, value)) in self.components.iter().enumerate() {
+            if i > 0 {
+                write!(f, ", ")?;
+            }
+            write!(f, "{}: {}", name, value)?;
+        }
+        write!(f, "}}")
+    }
+}
diff --git a/src/rules/graph.rs b/src/rules/graph.rs
index 5f922aad6..6bdba10a8 100644
--- a/src/rules/graph.rs
+++ b/src/rules/graph.rs
@@ -21,11 +21,9 @@ use petgraph::graph::{DiGraph, EdgeIndex, NodeIndex};
 use petgraph::visit::EdgeRef;
 use serde::Serialize;
 use std::any::Any;
-use std::collections::{BTreeMap, BTreeSet, HashMap, HashSet, VecDeque};
+use std::collections::{BTreeMap, HashMap, HashSet};
 use std::rc::Rc;
 
-type NodePathOrderKey<'a> = (usize, Vec<(&'static str, &'a BTreeMap<String, String>)>);
-
 /// A source/target pair from the reduction graph, returned by
 /// [`ReductionGraph::outgoing_reductions`] and [`ReductionGraph::incoming_reductions`].
 #[derive(Debug, Clone)]
@@ -61,6 +59,8 @@ pub(crate) struct ReductionGraphJson {
     pub(crate) nodes: Vec<NodeJson>,
     /// List of reduction edges.
     pub(crate) edges: Vec<EdgeJson>,
+    /// Catalog aliases grouped by problem family.
+    pub(crate) aliases: BTreeMap<String, Vec<String>>,
 }
 
 impl ReductionGraphJson {
@@ -84,12 +84,16 @@ pub(crate) struct NodeJson {
     pub(crate) name: String,
     /// Variant attributes as key-value pairs.
     pub(crate) variant: BTreeMap<String, String>,
+    /// Whether this is the family's declared default variant.
+    pub(crate) default: bool,
     /// Structural category declared by the problem schema.
     pub(crate) category: crate::registry::ProblemCategory,
     /// Relative rustdoc path (e.g., "models/graph/maximum_independent_set").
     pub(crate) doc_path: String,
     /// Worst-case time complexity expression (empty if not declared).
     pub(crate) complexity: String,
+    /// Full source domain, including parameters absent from edge formulas.
+    pub(crate) parameter_names: Vec<String>,
 }
 
 /// Internal reference to a problem variant, used as HashMap key.
@@ -546,68 +550,6 @@ impl ReductionGraph {
         ReductionPath { steps }
     }
 
-    fn node_path_order_key(&self, node_path: &[NodeIndex]) -> NodePathOrderKey<'_> {
-        (
-            node_path.len().saturating_sub(1),
-            node_path
-                .iter()
-                .map(|&idx| {
-                    let node = &self.nodes[self.graph[idx]];
-                    (node.name, &node.variant)
-                })
-                .collect(),
-        )
-    }
-
-    #[allow(clippy::too_many_arguments)]
-    fn shortest_node_path(
-        &self,
-        source: NodeIndex,
-        target: NodeIndex,
-        adjacency: &[Vec<NodeIndex>],
-        excluded_nodes: &HashSet<NodeIndex>,
-        excluded_edges: &HashSet<(NodeIndex, NodeIndex)>,
-        max_nodes: usize,
-    ) -> Option<Vec<NodeIndex>> {
-        if excluded_nodes.contains(&source) || max_nodes == 0 {
-            return None;
-        }
-        if source == target {
-            return Some(vec![source]);
-        }
-
-        let mut queue = VecDeque::from([(source, 1usize)]);
-        let mut parents = HashMap::new();
-        let mut visited = HashSet::from([source]);
-
-        while let Some((current, path_nodes)) = queue.pop_front() {
-            if path_nodes == max_nodes {
-                continue;
-            }
-            for &next in &adjacency[current.index()] {
-                if excluded_nodes.contains(&next)
-                    || excluded_edges.contains(&(current, next))
-                    || !visited.insert(next)
-                {
-                    continue;
-                }
-                parents.insert(next, current);
-                if next == target {
-                    let mut path = vec![target];
-                    let mut node = target;
-                    while node != source {
-                        node = parents[&node];
-                        path.push(node);
-                    }
-                    path.reverse();
-                    return Some(path);
-                }
-                queue.push_back((next, path_nodes + 1));
-            }
-        }
-        None
-    }
-
     fn find_k_shortest_node_paths(
         &self,
         source: NodeIndex,
@@ -616,69 +558,34 @@ impl ReductionGraph {
         limit: usize,
         max_nodes: usize,
     ) -> Vec<Vec<NodeIndex>> {
-        if source == target || limit == 0 {
-            return Vec::new();
-        }
-
         let mut adjacency = vec![Vec::new(); self.graph.node_count()];
         for node in self.graph.node_indices() {
             adjacency[node.index()] = self
                 .ordered_outgoing_edges(node, mode)
                 .into_iter()
-                .map(|(target, _)| target)
+                .map(|(target, _)| target.index())
                 .collect();
         }
-
-        let Some(first) = self.shortest_node_path(
-            source,
-            target,
+        let mut canonical: Vec<_> = self.graph.node_indices().collect();
+        canonical.sort_by_key(|&node| {
+            let variant = &self.nodes[self.graph[node]];
+            (variant.name, &variant.variant)
+        });
+        let mut order = vec![0; canonical.len()];
+        for (rank, node) in canonical.into_iter().enumerate() {
+            order[node.index()] = rank;
+        }
+        crate::path_search::find_paths(
             &adjacency,
-            &HashSet::new(),
-            &HashSet::new(),
+            &order,
+            source.index(),
+            target.index(),
+            limit,
             max_nodes,
-        ) else {
-            return Vec::new();
-        };
-
-        let mut accepted = vec![first];
-        let mut candidates = BTreeSet::new();
-
-        while accepted.len() < limit {
-            let previous = accepted.last().expect("accepted path exists");
-            for spur_index in 0..previous.len().saturating_sub(1) {
-                let root = &previous[..=spur_index];
-                let excluded_edges = accepted
-                    .iter()
-                    .filter(|path| path.len() > spur_index + 1 && path[..=spur_index] == *root)
-                    .map(|path| (path[spur_index], path[spur_index + 1]))
-                    .collect::<HashSet<_>>();
-                let excluded_nodes = root[..spur_index].iter().copied().collect();
-                let max_spur_nodes = max_nodes.saturating_sub(spur_index);
-                let Some(spur) = self.shortest_node_path(
-                    previous[spur_index],
-                    target,
-                    &adjacency,
-                    &excluded_nodes,
-                    &excluded_edges,
-                    max_spur_nodes,
-                ) else {
-                    continue;
-                };
-                let mut candidate = root[..spur_index].to_vec();
-                candidate.extend(spur);
-                if !accepted.contains(&candidate) {
-                    let key = self.node_path_order_key(&candidate);
-                    candidates.insert((key, candidate));
-                }
-            }
-
-            let Some((_, next)) = candidates.pop_first() else {
-                break;
-            };
-            accepted.push(next);
-        }
-
-        accepted
+        )
+        .into_iter()
+        .map(|path| path.into_iter().map(NodeIndex::new).collect())
+        .collect()
     }
 
     /// Find all simple paths between two specific problem variants.
@@ -974,6 +881,36 @@ impl ReductionGraph {
             .collect()
     }
 
+    /// Polynomial profile of a path: the composed transform's certificates over the
+    /// full source box, with nominal signed formulas kept for audit.
+    pub fn path_polynomial_profile(
+        &self,
+        path: &ReductionPath,
+    ) -> Result<crate::poly_compare::Profile, PathParameterError> {
+        let source = path.steps.first().ok_or(PathParameterError::EmptyPath)?;
+        let names = self.parameter_names(&source.name);
+        let steps = self.path_parameter_transforms(path)?;
+        let composed = match self.compose_transforms(path, &steps)? {
+            Some(composed) => composed,
+            None => crate::parameters::ParameterTransform::new(
+                source.name.clone(),
+                crate::parameters::ParameterRelation::Exact,
+                names
+                    .iter()
+                    .map(|name| (name.as_str(), crate::expr::Expr::variable(name.as_str()))),
+            )
+            .map_err(|error| PathParameterError::Step {
+                step: 0,
+                source_problem: source.name.clone(),
+                target_problem: source.name.clone(),
+                error: Box::new(error),
+            })?,
+        };
+        Ok(crate::poly_compare::Profile::from_path(
+            &names, &steps, &composed,
+        ))
+    }
+
     /// Compose symbolic parameter transforms along a path.
     pub fn compose_path_parameter_transform(
         &self,
@@ -982,19 +919,23 @@ impl ReductionGraph {
         if path.steps.is_empty() {
             return Err(PathParameterError::EmptyPath);
         }
-        if path.steps.len() == 1 {
-            return Ok(None);
-        }
+        self.compose_transforms(path, &self.path_parameter_transforms(path)?)
+    }
 
-        let mut transforms = self.path_parameter_transforms(path)?.into_iter();
-        let Some(mut composed) = transforms.next() else {
+    fn compose_transforms(
+        &self,
+        path: &ReductionPath,
+        transforms: &[crate::parameters::ParameterTransform],
+    ) -> Result<Option<crate::parameters::ParameterTransform>, PathParameterError> {
+        let Some((first, rest)) = transforms.split_first() else {
             return Ok(None);
         };
-        for (offset, transform) in transforms.enumerate() {
+        let mut composed = first.clone();
+        for (offset, transform) in rest.iter().enumerate() {
             let edge_index = offset + 1;
             composed = composed
                 .compose(
-                    &transform,
+                    transform,
                     format!(
                         "{} -> {}",
                         path.steps[0].name,
@@ -1350,9 +1291,11 @@ impl ReductionGraph {
                     NodeJson {
                         name: node.name.to_string(),
                         variant: node.variant.clone(),
+                        default: self.default_variants.get(node.name) == Some(&node.variant),
                         category,
                         doc_path: Self::doc_path_from_module_path(module_path, node.name),
                         complexity: node.complexity.to_string(),
+                        parameter_names: self.parameter_names(node.name),
                     },
                 )
             })
@@ -1437,7 +1380,32 @@ impl ReductionGraph {
                 ))
         });
 
-        ReductionGraphJson { nodes, edges }
+        let mut aliases: BTreeMap<String, Vec<String>> = inventory::iter::<ProblemSchemaEntry>
+            .into_iter()
+            .map(|entry| {
+                (
+                    entry.name.to_string(),
+                    entry
+                        .aliases
+                        .iter()
+                        .map(|alias| alias.to_string())
+                        .collect(),
+                )
+            })
+            .collect();
+        for entry in inventory::iter::<crate::registry::VariantEntry> {
+            let family = aliases.entry(entry.name.to_string()).or_default();
+            for alias in entry.aliases {
+                if !family.iter().any(|known| known.eq_ignore_ascii_case(alias)) {
+                    family.push(alias.to_string());
+                }
+            }
+        }
+        ReductionGraphJson {
+            nodes,
+            edges,
+            aliases,
+        }
     }
 
     /// Find the doc_path for a reduction entry matching the given source/target.
diff --git a/src/rules/unitdiskmapping/ksg/gadgets.rs b/src/rules/unitdiskmapping/ksg/gadgets.rs
index 4e64e7574..e97e8abf8 100644
--- a/src/rules/unitdiskmapping/ksg/gadgets.rs
+++ b/src/rules/unitdiskmapping/ksg/gadgets.rs
@@ -1662,17 +1662,6 @@ fn apply_gadget_boxed(pattern: &dyn KsgPatternBoxed, grid: &mut MappingGrid, i:
     }
 }
 
-/// Apply a boxed gadget pattern at position (i, j) with proper weights.
-#[allow(dead_code)]
-fn apply_weighted_gadget_boxed_fn(
-    pattern: &dyn KsgPatternBoxed,
-    grid: &mut MappingGrid,
-    i: usize,
-    j: usize,
-) {
-    pattern.apply_weighted_gadget_boxed(grid, i, j);
-}
-
 /// Trait for boxed pattern operations.
 pub trait KsgPatternBoxed {
     fn size_boxed(&self) -> (usize, usize);
diff --git a/src/rules/unitdiskmapping/triangular/mod.rs b/src/rules/unitdiskmapping/triangular/mod.rs
index 48e8ee381..92b864ef0 100644
--- a/src/rules/unitdiskmapping/triangular/mod.rs
+++ b/src/rules/unitdiskmapping/triangular/mod.rs
@@ -24,11 +24,5 @@ pub use gadgets::{
 };
 pub use mapping::{
     map_config_back, map_unit_weights, map_weighted, map_weighted_with_method,
-    map_weighted_with_order,
+    map_weighted_with_order, PADDING, SPACING,
 };
-
-/// Spacing between copy lines for triangular mapping.
-pub const SPACING: usize = 6;
-
-/// Padding around the grid for triangular mapping.
-pub const PADDING: usize = 2;
diff --git a/src/truth_table.rs b/src/truth_table.rs
deleted file mode 100644
index 517ab6f66..000000000
--- a/src/truth_table.rs
+++ /dev/null
@@ -1,291 +0,0 @@
-//! Truth table utilities for logic gadgets.
-//!
-//! This module provides a `TruthTable` type for representing boolean functions
-//! and their truth tables, useful for constructing logic gadgets in reductions.
-
-use bitvec::prelude::*;
-use serde::{Deserialize, Serialize};
-
-/// A truth table representing a boolean function.
-///
-/// The truth table stores the output for each possible input combination.
-/// For n input variables, there are 2^n rows in the table.
-#[derive(Debug, Clone, PartialEq, Eq)]
-pub struct TruthTable {
-    /// Number of input variables.
-    num_inputs: usize,
-    /// Output values for each input combination.
-    /// Index corresponds to input as binary number (LSB first).
-    outputs: BitVec,
-}
-
-/// Serialization-friendly representation of a TruthTable.
-#[derive(Serialize, Deserialize)]
-struct TruthTableSerde {
-    num_inputs: usize,
-    outputs: Vec<bool>,
-}
-
-impl Serialize for TruthTable {
-    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
-    where
-        S: serde::Serializer,
-    {
-        let serde_repr = TruthTableSerde {
-            num_inputs: self.num_inputs,
-            outputs: self.outputs.iter().by_vals().collect(),
-        };
-        serde_repr.serialize(serializer)
-    }
-}
-
-impl<'de> Deserialize<'de> for TruthTable {
-    fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
-    where
-        D: serde::Deserializer<'de>,
-    {
-        let serde_repr = TruthTableSerde::deserialize(deserializer)?;
-        TruthTable::try_from_outputs(serde_repr.num_inputs, serde_repr.outputs)
-            .map_err(serde::de::Error::custom)
-    }
-}
-
-impl TruthTable {
-    fn row_count(num_inputs: usize) -> Result<usize, crate::registry::ConstructionError> {
-        u32::try_from(num_inputs)
-            .ok()
-            .and_then(|shift| 1usize.checked_shl(shift))
-            .filter(|&rows| rows <= BitSlice::<usize, Lsb0>::MAX_BITS)
-            .ok_or_else(|| {
-                crate::registry::ConstructionError::IntegerOverflow(
-                    "representing truth-table rows".into(),
-                )
-            })
-    }
-
-    /// Create a truth table from a vector of boolean outputs.
-    ///
-    /// The outputs vector must have exactly 2^num_inputs elements.
-    /// Index i corresponds to the input where the j-th bit represents variable j.
-    pub fn from_outputs(num_inputs: usize, outputs: Vec<bool>) -> Self {
-        Self::try_from_outputs(num_inputs, outputs).unwrap_or_else(|error| panic!("{error}"))
-    }
-
-    fn try_from_outputs(
-        num_inputs: usize,
-        outputs: Vec<bool>,
-    ) -> Result<Self, crate::registry::ConstructionError> {
-        let expected_len = Self::row_count(num_inputs)?;
-        if outputs.len() != expected_len {
-            return Err(format!(
-                "outputs length must be 2^num_inputs = {}, got {}",
-                expected_len,
-                outputs.len()
-            )
-            .into());
-        }
-
-        let bits: BitVec = outputs.into_iter().collect();
-        Ok(Self {
-            num_inputs,
-            outputs: bits,
-        })
-    }
-
-    /// Create a truth table from a function.
-    ///
-    /// The function takes a slice of booleans (the input) and returns the output.
-    pub fn from_function<F>(num_inputs: usize, f: F) -> Self
-    where
-        F: Fn(&[bool]) -> bool,
-    {
-        let num_rows = Self::row_count(num_inputs).unwrap_or_else(|error| panic!("{error}"));
-        let mut outputs = BitVec::with_capacity(num_rows);
-
-        for i in 0..num_rows {
-            let input: Vec<bool> = (0..num_inputs).map(|j| (i >> j) & 1 == 1).collect();
-            outputs.push(f(&input));
-        }
-
-        Self {
-            num_inputs,
-            outputs,
-        }
-    }
-
-    /// Get the number of input variables.
-    pub fn num_inputs(&self) -> usize {
-        self.num_inputs
-    }
-
-    /// Get the number of rows (2^num_inputs).
-    pub fn num_rows(&self) -> usize {
-        self.outputs.len()
-    }
-
-    /// Evaluate the truth table for a given input.
-    pub fn evaluate(&self, input: &[bool]) -> bool {
-        assert_eq!(
-            input.len(),
-            self.num_inputs,
-            "input length must match num_inputs"
-        );
-
-        let index = Self::input_to_index(input);
-        self.outputs[index]
-    }
-
-    /// Evaluate using a usize config (0/1 values).
-    pub fn evaluate_config(&self, config: &[usize]) -> bool {
-        let input: Vec<bool> = config.iter().map(|&x| x != 0).collect();
-        self.evaluate(&input)
-    }
-
-    /// Convert an input to its index in the truth table.
-    fn input_to_index(input: &[bool]) -> usize {
-        input
-            .iter()
-            .enumerate()
-            .map(|(i, &b)| if b { 1 << i } else { 0 })
-            .sum()
-    }
-
-    /// Get the output values as a bitvec.
-    pub fn outputs(&self) -> &BitVec {
-        &self.outputs
-    }
-
-    /// Get all outputs as a vector of bools.
-    pub fn outputs_vec(&self) -> Vec<bool> {
-        self.outputs.iter().by_vals().collect()
-    }
-
-    /// Get the input configuration for a given row index.
-    pub fn index_to_input(&self, index: usize) -> Vec<bool> {
-        (0..self.num_inputs)
-            .map(|j| (index >> j) & 1 == 1)
-            .collect()
-    }
-
-    /// Count the number of true outputs.
-    pub fn count_ones(&self) -> usize {
-        self.outputs.count_ones()
-    }
-
-    /// Count the number of false outputs.
-    pub fn count_zeros(&self) -> usize {
-        self.outputs.count_zeros()
-    }
-
-    /// Check if the function is satisfiable (has at least one true output).
-    pub fn is_satisfiable(&self) -> bool {
-        self.outputs.any()
-    }
-
-    /// Check if the function is a tautology (all outputs are true).
-    pub fn is_tautology(&self) -> bool {
-        self.outputs.all()
-    }
-
-    /// Check if the function is a contradiction (all outputs are false).
-    pub fn is_contradiction(&self) -> bool {
-        self.outputs.not_any()
-    }
-
-    /// Get all satisfying assignments.
-    pub fn satisfying_assignments(&self) -> Vec<Vec<bool>> {
-        (0..self.num_rows())
-            .filter(|&i| self.outputs[i])
-            .map(|i| self.index_to_input(i))
-            .collect()
-    }
-
-    /// Create an AND gate truth table.
-    pub fn and(num_inputs: usize) -> Self {
-        Self::from_function(num_inputs, |input| input.iter().all(|&b| b))
-    }
-
-    /// Create an OR gate truth table.
-    pub fn or(num_inputs: usize) -> Self {
-        Self::from_function(num_inputs, |input| input.iter().any(|&b| b))
-    }
-
-    /// Create a NOT gate truth table (1 input).
-    pub fn not() -> Self {
-        Self::from_outputs(1, vec![true, false])
-    }
-
-    /// Create an XOR gate truth table.
-    pub fn xor(num_inputs: usize) -> Self {
-        Self::from_function(num_inputs, |input| {
-            input.iter().filter(|&&b| b).count() % 2 == 1
-        })
-    }
-
-    /// Create a NAND gate truth table.
-    pub fn nand(num_inputs: usize) -> Self {
-        Self::from_function(num_inputs, |input| !input.iter().all(|&b| b))
-    }
-
-    /// Create a NOR gate truth table.
-    pub fn nor(num_inputs: usize) -> Self {
-        Self::from_function(num_inputs, |input| !input.iter().any(|&b| b))
-    }
-
-    /// Create an XNOR gate truth table.
-    pub fn xnor(num_inputs: usize) -> Self {
-        Self::from_function(num_inputs, |input| {
-            input.iter().filter(|&&b| b).count().is_multiple_of(2)
-        })
-    }
-
-    /// Create an implication gate (a -> b = !a OR b).
-    /// Input 0 is 'a', input 1 is 'b'.
-    pub fn implies() -> Self {
-        // Index 0: [F,F] -> T, Index 1: [T,F] -> F, Index 2: [F,T] -> T, Index 3: [T,T] -> T
-        Self::from_outputs(2, vec![true, false, true, true])
-    }
-
-    /// Combine two truth tables using AND.
-    pub fn and_with(&self, other: &TruthTable) -> TruthTable {
-        assert_eq!(self.num_inputs, other.num_inputs);
-        let outputs: BitVec = self
-            .outputs
-            .iter()
-            .zip(other.outputs.iter())
-            .map(|(a, b)| *a && *b)
-            .collect();
-        TruthTable {
-            num_inputs: self.num_inputs,
-            outputs,
-        }
-    }
-
-    /// Combine two truth tables using OR.
-    pub fn or_with(&self, other: &TruthTable) -> TruthTable {
-        assert_eq!(self.num_inputs, other.num_inputs);
-        let outputs: BitVec = self
-            .outputs
-            .iter()
-            .zip(other.outputs.iter())
-            .map(|(a, b)| *a || *b)
-            .collect();
-        TruthTable {
-            num_inputs: self.num_inputs,
-            outputs,
-        }
-    }
-
-    /// Negate the truth table.
-    pub fn negate(&self) -> TruthTable {
-        let outputs: BitVec = self.outputs.iter().map(|b| !*b).collect();
-        TruthTable {
-            num_inputs: self.num_inputs,
-            outputs,
-        }
-    }
-}
-
-#[cfg(test)]
-#[path = "unit_tests/truth_table.rs"]
-mod tests;
diff --git a/src/types.rs b/src/types.rs
index 10d27bdcb..c91566378 100644
--- a/src/types.rs
+++ b/src/types.rs
@@ -705,92 +705,7 @@ impl<V: fmt::Display> fmt::Display for Extremum<V> {
     }
 }
 
-/// Canonical named parameters for one concrete problem instance.
-#[derive(Debug, Clone, Default, PartialEq, Eq, Serialize, Deserialize)]
-pub struct ProblemParameters {
-    /// Named parameters in canonical declaration order.
-    #[serde(deserialize_with = "deserialize_parameter_components")]
-    pub(crate) components: Vec<(String, u64)>,
-}
-
-impl ProblemParameters {
-    /// Create problem parameters in canonical declaration order.
-    ///
-    /// # Panics
-    /// Panics if a parameter name occurs more than once.
-    pub fn new(components: Vec<(&str, u64)>) -> Self {
-        Self::from_owned(
-            components
-                .into_iter()
-                .map(|(name, value)| (name.to_string(), value))
-                .collect(),
-        )
-    }
-
-    /// Create problem parameters from owned names.
-    ///
-    /// # Panics
-    /// Panics if a parameter name occurs more than once.
-    pub fn from_owned(components: Vec<(String, u64)>) -> Self {
-        if let Some(name) = duplicate_parameter_name(&components) {
-            panic!("duplicate problem parameter `{name}`");
-        }
-        Self { components }
-    }
-
-    /// Iterate over parameters in canonical declaration order.
-    pub fn iter(&self) -> impl Iterator<Item = (&str, u64)> {
-        self.components
-            .iter()
-            .map(|(name, value)| (name.as_str(), *value))
-    }
-
-    /// Get a parameter by name.
-    pub fn get(&self, name: &str) -> Option<u64> {
-        self.components
-            .iter()
-            .find(|(k, _)| k == name)
-            .map(|(_, v)| *v)
-    }
-}
-
-fn duplicate_parameter_name(components: &[(String, u64)]) -> Option<&str> {
-    components
-        .iter()
-        .enumerate()
-        .find_map(|(index, (name, _))| {
-            components[..index]
-                .iter()
-                .any(|(previous, _)| previous == name)
-                .then_some(name.as_str())
-        })
-}
-
-fn deserialize_parameter_components<'de, D>(deserializer: D) -> Result<Vec<(String, u64)>, D::Error>
-where
-    D: serde::Deserializer<'de>,
-{
-    let components = Vec::<(String, u64)>::deserialize(deserializer)?;
-    if let Some(name) = duplicate_parameter_name(&components) {
-        return Err(serde::de::Error::custom(format!(
-            "duplicate problem parameter `{name}`"
-        )));
-    }
-    Ok(components)
-}
-
-impl fmt::Display for ProblemParameters {
-    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
-        write!(f, "ProblemParameters{{")?;
-        for (i, (name, value)) in self.components.iter().enumerate() {
-            if i > 0 {
-                write!(f, ", ")?;
-            }
-            write!(f, "{}: {}", name, value)?;
-        }
-        write!(f, "}}")
-    }
-}
+pub use crate::problem_parameters::ProblemParameters;
 
 use crate::impl_variant_param;
 
diff --git a/src/unit_tests/models/misc/factoring.rs b/src/unit_tests/models/misc/factoring.rs
index 61bf2f201..071bc614b 100644
--- a/src/unit_tests/models/misc/factoring.rs
+++ b/src/unit_tests/models/misc/factoring.rs
@@ -39,15 +39,6 @@ fn test_bits_to_biguint() {
     assert_eq!(bits_to_biguint(&[1, 1, 1]), BigUint::from(7u32));
 }
 
-#[test]
-fn test_int_to_bits() {
-    assert_eq!(int_to_bits(&BigUint::from(0u32), 3), vec![0, 0, 0]);
-    assert_eq!(int_to_bits(&BigUint::from(1u32), 3), vec![1, 0, 0]);
-    assert_eq!(int_to_bits(&BigUint::from(2u32), 3), vec![0, 1, 0]);
-    assert_eq!(int_to_bits(&BigUint::from(3u32), 3), vec![1, 1, 0]);
-    assert_eq!(int_to_bits(&BigUint::from(7u32), 3), vec![1, 1, 1]);
-}
-
 #[test]
 fn test_read_factors() {
     let problem = Factoring::with_factor_bits(6, 2, 2);
@@ -58,14 +49,6 @@ fn test_read_factors() {
     assert_eq!(b, BigUint::from(3u32));
 }
 
-#[test]
-fn test_is_factoring_function() {
-    assert!(is_factoring(&6u32.into(), &2u32.into(), &3u32.into()));
-    assert!(is_factoring(&6u32.into(), &3u32.into(), &2u32.into()));
-    assert!(is_factoring(&15u32.into(), &3u32.into(), &5u32.into()));
-    assert!(!is_factoring(&6u32.into(), &2u32.into(), &2u32.into()));
-}
-
 #[test]
 fn test_is_valid_factorization() {
     let problem = Factoring::with_factor_bits(6, 2, 2);
diff --git a/src/unit_tests/parameters.rs b/src/unit_tests/parameters.rs
index 908a9946c..ee745b96f 100644
--- a/src/unit_tests/parameters.rs
+++ b/src/unit_tests/parameters.rs
@@ -2,6 +2,47 @@ use super::{ParameterRelation, ParameterTransform, ParameterTransformError};
 use crate::expr::Expr;
 use crate::types::ProblemParameters;
 
+#[test]
+fn partial_hull_preserves_exact_negative_terms_and_bounds_uncertain_inputs() {
+    let first = ParameterTransform::from_fields(
+        "first",
+        [
+            ("v", ParameterRelation::Exact, Expr::parse("n")),
+            ("e", ParameterRelation::UpperBound, Expr::parse("n^2")),
+        ],
+    )
+    .unwrap();
+    let next = ParameterTransform::new(
+        "next",
+        ParameterRelation::Exact,
+        [
+            ("complement", Expr::parse("v*(v-1)/2-e")),
+            ("constant", Expr::parse("10-e")),
+            ("exact", Expr::parse("v*(v-1)/2")),
+            ("mixed", Expr::parse("e+v^3-v-v*e")),
+            ("cancelled", Expr::parse("(e+v)^2-e^2-2*e*v")),
+        ],
+    )
+    .unwrap();
+    let composed = first.compose(&next, "composed").unwrap();
+    for (field, value, relation) in [
+        ("complement", 6, ParameterRelation::UpperBound),
+        ("constant", 10, ParameterRelation::UpperBound),
+        ("exact", 6, ParameterRelation::Exact),
+        ("mixed", 76, ParameterRelation::UpperBound),
+        ("cancelled", 16, ParameterRelation::Exact),
+    ] {
+        assert_eq!(composed.relation(field), Some(relation));
+        assert_eq!(
+            composed
+                .evaluate(&ProblemParameters::new(vec![("n", 4)]))
+                .unwrap()
+                .get(field),
+            Some(value)
+        );
+    }
+}
+
 #[test]
 fn composition_preserves_fields_with_available_dependencies() {
     let first = ParameterTransform::new(
diff --git a/src/unit_tests/poly_compare.rs b/src/unit_tests/poly_compare.rs
new file mode 100644
index 000000000..374350c39
--- /dev/null
+++ b/src/unit_tests/poly_compare.rs
@@ -0,0 +1,629 @@
+use super::*;
+use crate::parameters::{ParameterRelation, ParameterTransform, ParameterTransformError};
+
+fn poly(s: &str) -> Poly {
+    Poly::from_expr(&Expr::parse(s)).unwrap()
+}
+fn field(s: &str) -> FieldCertificate {
+    FieldCertificate::new(&Expr::parse(s), ParameterRelation::Exact)
+}
+fn pair(f: &str, g: &str) -> FieldComparison {
+    compare(&field(f), &field(g), &BTreeSet::new())
+}
+fn certificate(p: &Profile, name: &str) -> Option<(Poly, ParameterRelation)> {
+    p.fields[name].certificate.clone().ok()
+}
+
+#[test]
+fn signed_polynomials_with_matching_positive_supports_are_equivalent() {
+    for (f, g) in [
+        ("n^2+m^2-n*m", "n^2+m^2"),
+        ("n*(n-1)/2-m", "n^2"), // Zero on complete graphs; its positive part is quadratic.
+    ] {
+        let c = pair(f, g);
+        assert_eq!(c.verdict(), Verdict::Equivalent);
+        let Direction::Yes(proof) = c.forward else {
+            panic!("the positive denominator covers the signed numerator")
+        };
+        assert!(proof.verify(&poly(f), &poly(g)));
+    }
+}
+
+#[test]
+fn identical_signed_formulas_and_zero_have_direct_proofs() {
+    let c = pair("n-m", "n-m");
+    assert_eq!(c.verdict(), Verdict::Equivalent);
+    for d in [c.forward, c.reverse] {
+        let Direction::Yes(proof @ GenericProof::Identity) = d else {
+            panic!("signed identity must be certified")
+        };
+        assert!(proof.verify(&poly("n-m"), &poly("n-m")));
+        assert!(!proof.verify(&poly("n-m"), &poly("n+m")));
+    }
+    let Direction::Yes(proof @ GenericProof::Zero) = pair("0", "n-m").forward else {
+        panic!("zero is bounded by every declared nonnegative certificate")
+    };
+    assert!(proof.verify(&poly("0"), &poly("n-m")));
+    assert!(!proof.verify(&poly("n"), &poly("n-m")));
+}
+
+#[test]
+fn witnesses_reject_negative_and_cancelled_top_faces() {
+    let curve = BTreeMap::from([
+        (Symbol::new("n").unwrap(), (2u8.into(), 1u8.into())),
+        (Symbol::new("m").unwrap(), (2u8.into(), 2u8.into())),
+    ]);
+    for (f, g) in [("n-m", "1"), ("n^3", "n-m")] {
+        let f = poly(f);
+        let g = poly(g);
+        let witness = Witness {
+            curve: curve.clone(),
+            numerator: on_curve(&f, &curve).unwrap(),
+            denominator: on_curve(&g, &curve).unwrap(),
+        };
+        assert!(!witness.verify(&f, &g, &[]));
+        assert!(Witness::on(curve.clone(), &f, &g, &[]).is_none());
+    }
+    let f = poly("m^2-n");
+    let g = poly("m-n");
+    assert!(Witness::on(curve.clone(), &f, &g, &[])
+        .unwrap()
+        .verify(&f, &g, &[]));
+    let zero = poly("m-n^2/2");
+    assert!(Witness::on(curve.clone(), &f, &zero, &[]).is_none());
+    let zero = poly("0");
+    assert!(Witness::on(curve, &f, &zero, &[])
+        .unwrap()
+        .verify(&f, &zero, &[]));
+    let c = pair("n^3-m", "n-m");
+    let Direction::No(w) = c.forward else {
+        panic!("n grows while m stays bounded, with both leading coefficients positive")
+    };
+    assert!(w.verify(&poly("n^3-m"), &poly("n-m"), &[]));
+    // The constant term has no separating ray; a later mixed term does.
+    let c = pair("1+n*m^2", "n^2+m^2-n*m");
+    let Direction::No(w) = c.forward else {
+        panic!("search all positive numerator monomials")
+    };
+    assert!(w.verify(&poly("1+n*m^2"), &poly("n^2+m^2-n*m"), &[]));
+}
+
+#[test]
+fn exact_expansion_preserves_cancellation_and_rational_coefficients() {
+    assert_eq!(poly("n + m - m"), poly("n"));
+    assert_eq!(poly("(n+m)^2/2"), poly("n^2/2+n*m+m^2/2"));
+    for s in ["n/m", "sqrt(n)", "log(n)", "2^n", "factorial(n)"] {
+        assert_eq!(Poly::from_expr(&Expr::parse(s)), None);
+        assert!(matches!(
+            field(s).certificate,
+            Err(Reason::NotPolynomial(_))
+        ));
+    }
+}
+
+#[test]
+fn running_map_composes_exactly_and_keeps_signed_provenance() {
+    let f = ParameterTransform::new(
+        "map",
+        ParameterRelation::Exact,
+        [("n", Expr::parse("n+m")), ("m", Expr::parse("n*m"))],
+    )
+    .unwrap();
+    let source = ["n".to_string(), "m".to_string()];
+    let p = Profile::from_path(
+        &source,
+        &[f.clone(), f.clone()],
+        &f.compose(&f, "c").unwrap(),
+    );
+    assert_eq!(p.fields["n"].original_signed, Some(poly("n+m+n*m")));
+    assert_eq!(
+        certificate(&p, "m"),
+        Some((poly("n^2*m+n*m^2"), ParameterRelation::Exact))
+    );
+    let bounded = ParameterTransform::new(
+        "bound",
+        ParameterRelation::UpperBound,
+        [("n", Expr::parse("n")), ("m", Expr::parse("m"))],
+    )
+    .unwrap();
+    let outer = ParameterTransform::new(
+        "signed",
+        ParameterRelation::Exact,
+        [("size", Expr::parse("n*m-n"))],
+    )
+    .unwrap();
+    let composed = bounded.compose(&outer, "c").unwrap();
+    let p = Profile::from_path(&source, &[bounded, outer], &composed);
+    assert_eq!(p.fields["size"].original_signed, Some(poly("n*m-n")));
+    assert_eq!(
+        certificate(&p, "size"),
+        Some((poly("n*m"), ParameterRelation::UpperBound))
+    );
+}
+
+#[test]
+fn partial_hull_keeps_negative_terms_over_exact_inputs() {
+    let first = ParameterTransform::from_fields(
+        "first",
+        [
+            ("v", ParameterRelation::Exact, Expr::parse("n")),
+            ("e", ParameterRelation::UpperBound, Expr::parse("n^2")),
+        ],
+    )
+    .unwrap();
+    let next = ParameterTransform::new(
+        "next",
+        ParameterRelation::Exact,
+        [
+            ("kept", Expr::parse("e + v^3 - v")),
+            ("dropped", Expr::parse("v^2 - e")),
+        ],
+    )
+    .unwrap();
+    let p = Profile::from_transform(&first.compose(&next, "c").unwrap());
+    assert_eq!(
+        certificate(&p, "kept"),
+        Some((poly("n^2+n^3-n"), ParameterRelation::UpperBound))
+    );
+    assert_eq!(
+        certificate(&p, "dropped"),
+        Some((poly("n^2"), ParameterRelation::UpperBound))
+    );
+}
+
+#[test]
+fn normalized_dependencies_do_not_lose_exactness() {
+    let first = ParameterTransform::new(
+        "first",
+        ParameterRelation::UpperBound,
+        [("m", Expr::parse("n^2"))],
+    )
+    .unwrap();
+    let next = ParameterTransform::new(
+        "next",
+        ParameterRelation::Exact,
+        [("size", Expr::parse("(m+1)^2-m^2-2*m"))],
+    )
+    .unwrap();
+    let p = Profile::from_transform(&first.compose(&next, "composed").unwrap());
+    assert_eq!(
+        certificate(&p, "size"),
+        Some((poly("1"), ParameterRelation::Exact))
+    );
+}
+
+#[test]
+fn newton_lp_decides_convex_supports_and_proven_incomparability() {
+    assert_eq!(
+        pair("n*m", "n^2+m^2").verdict(),
+        Verdict::Dominated { worse: Side::Right }
+    );
+    let c = pair("n", "m");
+    assert_eq!(c.verdict(), Verdict::Incomparable);
+    for (d, f, g) in [
+        (&c.forward, poly("n"), poly("m")),
+        (&c.reverse, poly("m"), poly("n")),
+    ] {
+        let Direction::No(w) = d else {
+            panic!("expected witness")
+        };
+        assert!(w.verify(&f, &g, &[]));
+    }
+}
+
+#[test]
+fn newton_coverage_ignores_dominated_support_terms() {
+    // AM-GM gives n^8*m^8 <= (n^16+m^16)/2; lower terms cannot invalidate it.
+    let lower_terms = (0..=6)
+        .flat_map(|a| (0..=6 - a).map(move |b| format!("n^{a}*m^{b}")))
+        .collect::<Vec<_>>()
+        .join("+");
+    let denominator = format!("n^16+m^16+{lower_terms}");
+    let comparison = pair("n^8*m^8", &denominator);
+    let Direction::Yes(proof) = comparison.forward else {
+        panic!("redundant support must not exhaust the coverage LP");
+    };
+    assert!(proof.verify(&poly("n^8*m^8"), &poly(&denominator)));
+    // All these points are coordinatewise maximal, but lie on the segment
+    // between n^32 and m^32. None is the numerator's (16,16) point.
+    let redundant = (0..=32)
+        .filter(|&a| a != 16)
+        .map(|a| format!("n^{a}*m^{}", 32 - a))
+        .collect::<Vec<_>>()
+        .join("+");
+    let comparison = pair("n^16*m^16", &redundant);
+    let Direction::Yes(proof) = comparison.forward else {
+        panic!("convex support redundancy must not exhaust the coverage LP");
+    };
+    assert!(proof.verify(&poly("n^16*m^16"), &poly(&redundant)));
+}
+
+#[test]
+fn axis_simplex_coverage_has_exact_multivariate_weights() {
+    let f = "(n+m+1)^6";
+    let g = "(n+m)^6+r*(n+m)^5+r^2*(n+m)^4+r^3*(n+m)^3+r^4*(n+m)^2+r^4";
+    let comparison = pair(f, g);
+    let Direction::Yes(proof) = comparison.forward else {
+        panic!("extra denominator support must not obscure axis-simplex coverage");
+    };
+    assert!(proof.verify(&poly(f), &poly(g)));
+    let variables = ["a", "b", "c", "d", "e", "f", "g", "h", "i"];
+    let numerator = variables.join("*");
+    let denominator = variables
+        .iter()
+        .map(|v| format!("{v}^9"))
+        .collect::<Vec<_>>()
+        .join("+");
+    let comparison = pair(&numerator, &denominator);
+    let Direction::Yes(proof) = comparison.forward else {
+        panic!("AM-GM proves coverage by the axis simplex");
+    };
+    assert!(proof.verify(&poly(&numerator), &poly(&denominator)));
+}
+
+#[test]
+fn summary_preserves_pair_counts_front_and_batch_validity() {
+    let mut missing = profile("n");
+    missing.fields.get_mut("size").unwrap().certificate = Err(Reason::MissingField);
+    let mut unused_coordinate = profile("1");
+    unused_coordinate.domain.insert(Symbol::new("m").unwrap());
+    let profiles = vec![
+        profile("n"),
+        profile("m"),
+        profile("2*n+1"),
+        profile("n-m"),
+        missing.clone(),
+        profile("n"),
+        missing,
+        profile("0"),
+        unused_coordinate,
+        profile("1"),
+    ];
+    let full = compare_all(&profiles);
+    let summary = compare_summary(&profiles);
+    assert_eq!(summary.counts, full.counts());
+    assert_eq!(summary.front, full.front);
+    assert_eq!(summary.counts.iter().sum::<usize>(), 45);
+    let batch = batch_certificates(&profiles);
+    for (i, j, pair) in &full.pairs {
+        for (name, comparison) in &pair.fields {
+            if let (Ok(f), Ok(g)) = (
+                profiles[*i].fields[name].poly(),
+                profiles[*j].fields[name].poly(),
+            ) {
+                for (direction, f, g) in [(&comparison.forward, f, g), (&comparison.reverse, g, f)]
+                {
+                    match direction {
+                        Direction::Yes(proof) => assert!(proof.verify(f, g)),
+                        Direction::No(witness) => assert!(witness.verify(f, g, &batch)),
+                        Direction::Unknown(_) => {}
+                    }
+                }
+            }
+        }
+    }
+    assert_eq!(compare_summary(&[]).counts, [0; 4]);
+    assert!(compare_summary(&[]).front.is_empty());
+}
+
+#[test]
+fn signed_support_coverage_ignores_exceptional_cancellations() {
+    assert_eq!(pair("n*m-n*m/4", "n*m").verdict(), Verdict::Equivalent);
+    assert_eq!(pair("n*m-n", "n*m").verdict(), Verdict::Equivalent);
+    assert_eq!(
+        pair("n^2*m^2-100*n*m", "n^2*m^2").verdict(),
+        Verdict::Equivalent
+    );
+    assert_eq!(
+        pair("n^2+m^2-n*m", "n^2+m^2").verdict(),
+        Verdict::Equivalent
+    );
+    assert_eq!(pair("n^2-m", "n^2").verdict(), Verdict::Equivalent);
+    let c = pair("n*m-2*n", "n*m");
+    assert_eq!(c.verdict(), Verdict::Equivalent);
+}
+
+#[test]
+fn signed_monotone_suffix_reversal_keeps_all_prefixes() {
+    let prefix = |y: &str, z: &str| {
+        ParameterTransform::new(
+            "prefix",
+            ParameterRelation::Exact,
+            [("y", Expr::parse(y)), ("z", Expr::parse(z))],
+        )
+        .unwrap()
+    };
+    let (u, v) = (prefix("3", "n"), prefix("2", "n^2"));
+    assert_eq!(
+        compare_profiles(&Profile::from_transform(&u), &Profile::from_transform(&v)).verdict,
+        Verdict::Dominated { worse: Side::Right }
+    );
+    let suffix = ParameterTransform::new(
+        "suffix",
+        ParameterRelation::Exact,
+        [("size", Expr::parse("(y-2)*z"))],
+    )
+    .unwrap();
+    let completed = [&u, &v].map(|p| Profile::from_transform(&p.compose(&suffix, "c").unwrap()));
+    assert_eq!(compare_all(&completed).front, vec![1]);
+    // Both prefixes must be extended: pruning v would delete the optimal zero completion.
+    assert_eq!(
+        certificate(&completed[1], "size"),
+        Some((poly("0"), ParameterRelation::Exact))
+    );
+}
+
+#[test]
+fn kleene_profiles_preserve_unknown_and_equivalent_candidates() {
+    let p = Profile::new(BTreeMap::from([("a".into(), field("n"))]));
+    let q = Profile::new(BTreeMap::from([
+        ("a".into(), field("m")),
+        ("b".into(), field("n")),
+    ]));
+    assert_eq!(compare_profiles(&p, &q).verdict, Verdict::Incomparable);
+    let all = compare_all(&[p.clone(), p.clone(), q]);
+    assert_eq!(all.front, vec![0, 1, 2]);
+    assert_eq!(all.counts(), [0, 1, 2, 0]);
+    assert!(matches!(
+        pair("n", "log(n)").forward,
+        Direction::Unknown(Reason::NotPolynomial(_))
+    ));
+}
+
+#[test]
+fn unused_source_coordinates_remain_in_signed_profiles() {
+    let p = Profile::from_transform(
+        &ParameterTransform::new(
+            "source",
+            ParameterRelation::Exact,
+            [("a", Expr::parse("n^2-100*n")), ("b", Expr::parse("m"))],
+        )
+        .unwrap(),
+    );
+    let q = Profile::from_transform(
+        &ParameterTransform::new(
+            "source",
+            ParameterRelation::Exact,
+            [("a", Expr::parse("n^2")), ("b", Expr::parse("m"))],
+        )
+        .unwrap(),
+    );
+    assert_eq!(compare_profiles(&p, &q).verdict, Verdict::Equivalent);
+    assert!(p.domain.contains(&Symbol::new("m").unwrap()));
+}
+
+#[test]
+fn unavailable_dependencies_are_checked_after_cancellation() {
+    let mut first = ParameterTransform::new(
+        "missing",
+        ParameterRelation::Exact,
+        [("n", Expr::parse("n"))],
+    )
+    .unwrap();
+    first.declare_unavailable("m", "not registered");
+    let next = ParameterTransform::new(
+        "outer",
+        ParameterRelation::Exact,
+        [
+            ("a", Expr::parse("n-m")),
+            ("b", Expr::parse("(m+1)^2-m^2-2*m")),
+        ],
+    )
+    .unwrap();
+    let result = Profile::from_transform(&first.compose(&next, "c").unwrap());
+    assert!(matches!(
+        result.fields["a"].certificate,
+        Err(Reason::Unavailable(
+            ParameterTransformError::UnavailableInput { .. }
+        ))
+    ));
+    assert_eq!(
+        certificate(&result, "b"),
+        Some((poly("1"), ParameterRelation::Exact))
+    );
+}
+
+#[test]
+fn proof_verifiers_reject_tampered_weights_and_curves() {
+    let c = pair("n*m", "n^2+m^2");
+    let Direction::Yes(mut proof) = c.forward else {
+        panic!("convex proof")
+    };
+    assert!(proof.verify(&poly("n*m"), &poly("n^2+m^2")));
+    if let GenericProof::Newton(coverage) = &mut proof {
+        coverage[0].weights[0].1 += BigRational::one();
+    }
+    assert!(!proof.verify(&poly("n*m"), &poly("n^2+m^2")));
+    let c = pair("n", "m");
+    let Direction::No(mut w) = c.forward else {
+        panic!("curve")
+    };
+    w.numerator.clear();
+    assert!(!w.verify(&poly("n"), &poly("m"), &[]));
+}
+
+#[test]
+fn exact_lp_finds_fractional_points_and_rejects_infeasibility() {
+    let r = |v: i64| BigRational::from_integer(v.into());
+    let feasible = lp::feasible(&[vec![r(-3)], vec![r(2)]], &[r(-1), r(1)])
+        .unwrap()
+        .unwrap();
+    assert_eq!(feasible, vec![BigRational::new(1.into(), 3.into())]);
+    assert_eq!(
+        lp::feasible(&[vec![r(-1)], vec![r(1)]], &[r(-2), r(1)]).unwrap(),
+        None
+    );
+    assert!(matches!(
+        lp::feasible(&[vec![r(1); 25]], &[r(1)]),
+        Err(Reason::ResourceLimit(_))
+    ));
+}
+
+proptest::proptest! {
+    #![proptest_config(proptest::test_runner::Config::with_cases(64))]
+    #[test]
+    fn generated_decisions_have_exact_certificates_and_sample_bounds(
+        a in 0u8..4, b in 0u8..4, c in 0u8..4, d in 0u8..4,
+        coefficient in 1u8..6, n in 2u64..9, m in 2u64..9) {
+        let f = format!("{coefficient}*n^{a}*m^{b}+1");
+        let g = format!("n^{c}*m^{d}+n^2+m^2+1");
+        let pf=poly(&f); let pg=poly(&g);
+        let comparison=pair(&f,&g);
+        let values=crate::types::ProblemParameters::new(vec![("n",n),("m",m)]);
+        let evaluate = |s:&str| ParameterTransform::new("sample",ParameterRelation::Exact,[("value",Expr::parse(s))]).unwrap().evaluate(&values).unwrap().get("value").unwrap();
+        for (direction,p,q,ps,qs) in [(&comparison.forward,&pf,&pg,f.as_str(),g.as_str()),(&comparison.reverse,&pg,&pf,g.as_str(),f.as_str())] {
+            match direction {
+                Direction::Yes(proof) => {
+                    proptest::prop_assert!(proof.verify(p,q));
+                    // All generated denominator coefficients are >= 1. Weighted AM-GM bounds each covered monomial by q.
+                    let bound: BigRational=p.terms().values().sum();
+                    proptest::prop_assert!(BigRational::from_integer(evaluate(ps).into()) <= bound*BigRational::from_integer(evaluate(qs).into()));
+                }
+                Direction::No(w) => proptest::prop_assert!(w.verify(p,q,&[pf.clone(),pg.clone()])),
+                Direction::Unknown(_) => {}
+            }
+
+        }
+        // Re-check shared batch results independently, including a signed validity guard.
+        let batch = [pf, pg, poly("n-m")];
+        let profiles = [profile(&f), profile(&g), profile("n-m")];
+        let full = compare_all(&profiles);
+        let summary = compare_summary(&profiles);
+        proptest::prop_assert_eq!(summary.counts, full.counts());
+        proptest::prop_assert_eq!(summary.front, full.front.clone());
+        for (i,j,comparison) in full.pairs {
+            for (direction,p,q) in [(&comparison.fields["size"].forward,&batch[i],&batch[j]),
+                                    (&comparison.fields["size"].reverse,&batch[j],&batch[i])] {
+                match direction {
+                    Direction::Yes(proof) => proptest::prop_assert!(proof.verify(p,q)),
+                    Direction::No(witness) => proptest::prop_assert!(witness.verify(p,q,&batch)),
+                    Direction::Unknown(_) => {}
+                }
+            }
+        }
+    }
+}
+
+fn profile(s: &str) -> Profile {
+    Profile::new(BTreeMap::from([("size".into(), field(s))]))
+}
+fn curve(n: (u8, u8), m: (u8, u8)) -> Curve {
+    BTreeMap::from([
+        (Symbol::new("n").unwrap(), (n.0.into(), n.1.into())),
+        (Symbol::new("m").unwrap(), (m.0.into(), m.1.into())),
+    ])
+}
+
+#[test]
+fn complement_edges_have_direct_newton_coverage() {
+    let f = poly("n");
+    let g = poly("n*(n-1)/2-m");
+    let c = pair("n", "n*(n-1)/2-m");
+    let Direction::Yes(proof @ GenericProof::Newton(_)) = c.forward else {
+        panic!("generic coverage")
+    };
+    assert!(proof.verify(&f, &g));
+    assert!(!proof.verify(&poly("n^3"), &g));
+}
+
+#[test]
+fn exceptional_worst_case_witness_is_not_a_generic_refutation() {
+    let f = poly("n");
+    let g = poly("(n-m)^2+1");
+    let witness = Witness {
+        curve: curve((2, 1), (2, 1)),
+        numerator: BTreeMap::from([(1u8.into(), BigRational::from_integer(2.into()))]),
+        denominator: BTreeMap::from([(0u8.into(), BigRational::one())]),
+    };
+    assert!(!witness.verify(&f, &g, &[f.clone(), g.clone()]));
+    let Direction::Yes(proof) = pair("n", "(n-m)^2+1").forward else {
+        panic!("exceptional unbounded ratios must allow generic Yes")
+    };
+    assert!(proof.verify(&f, &g));
+}
+
+#[test]
+fn regular_witnesses_keep_bounded_strata_and_reject_invalid_batch_faces() {
+    let f = poly("n*m");
+    let g = poly("n^2");
+    let w = Witness::on(curve((2, 0), (2, 1)), &f, &g, &[]).unwrap();
+    assert!(w.verify(&f, &g, &[f.clone(), g.clone()]));
+    assert!(!w.verify(&f, &g, &[poly("n-m")]));
+    assert!(!w.verify(&f, &g, &[poly("n-2")]));
+    assert!(!w.verify(&f, &g, &[poly("k")]));
+    assert!(matches!(pair("n*m", "n^2").forward, Direction::No(_)));
+    let mut tampered = w;
+    tampered.numerator.clear();
+    assert!(!tampered.verify(&f, &g, &[]));
+}
+
+#[test]
+fn transitivity_and_zero_certificates_preserve_the_front() {
+    let profiles = [profile("n"), profile("n^2"), profile("n^3")];
+    let result = compare_all(&profiles);
+    assert_eq!(result.counts(), [3, 0, 0, 0]);
+    assert_eq!(result.front, vec![0]);
+    for (i, j, c) in &result.pairs {
+        let Direction::Yes(p) = &c.fields["size"].forward else {
+            panic!("transitive exponent order")
+        };
+        assert!(p.verify(
+            profiles[*i].fields["size"].poly().unwrap(),
+            profiles[*j].fields["size"].poly().unwrap()
+        ));
+    }
+    let result = compare_all(&[profile("n^2"), profile("0"), profile("n")]);
+    assert_eq!(result.front, vec![1]);
+    let c = &result.pairs[0].2.fields["size"];
+    assert!(matches!(c.forward, Direction::No(_)));
+    assert!(matches!(c.reverse, Direction::Yes(_)));
+    assert_eq!(
+        compare_all(&[profile("0"), profile("0")]).counts(),
+        [0, 1, 0, 0]
+    );
+}
+
+#[test]
+fn adding_a_path_changes_the_common_valid_family_set() {
+    let profiles = [profile("m"), profile("n"), profile("n-m")];
+    assert_eq!(
+        compare_profiles(&profiles[0], &profiles[1]).verdict,
+        Verdict::Incomparable
+    );
+    let result = compare_all(&profiles);
+    assert_eq!(result.pairs[0].2.verdict, Verdict::Unknown);
+    assert_eq!(
+        result.pairs[0].2.fields["size"].forward,
+        Direction::Unknown(Reason::Validity)
+    );
+}
+
+#[test]
+fn alternative_scales_find_a_regular_family_with_a_bounded_parameter() {
+    let profile = |size| {
+        Profile::new(BTreeMap::from([
+            ("size".into(), field(size)),
+            ("guard".into(), field("k-3")),
+        ]))
+    };
+    let c = compare_profiles(&profile("n^2"), &profile("n*k^2"));
+    let Direction::No(w) = &c.fields["size"].forward else {
+        panic!("perturb the bounded scale away from an invalid face")
+    };
+    assert!(w.verify(&poly("n^2"), &poly("n*k^2"), &[poly("k-3")]));
+}
+
+#[test]
+fn lower_dimensional_cell_search_checks_the_whole_batch_fan() {
+    let profile = |size| {
+        Profile::new(BTreeMap::from([
+            ("size".into(), field(size)),
+            ("guard".into(), field("512*m^5-n^13")),
+        ]))
+    };
+    let c = compare_profiles(&profile("n^3*m^3"), &profile("n^10+m^4"));
+    let Direction::No(w) = &c.fields["size"].forward else {
+        panic!("the batch face 5*e_m=13*e_n has a regular refutation")
+    };
+    assert!(w.verify(&poly("n^3*m^3"), &poly("n^10+m^4"), &[poly("512*m^5-n^13")]));
+}
diff --git a/src/unit_tests/poly_compare_render.rs b/src/unit_tests/poly_compare_render.rs
new file mode 100644
index 000000000..8d5a6b7af
--- /dev/null
+++ b/src/unit_tests/poly_compare_render.rs
@@ -0,0 +1,116 @@
+use super::*;
+
+fn field(s: &str) -> FieldCertificate {
+    FieldCertificate::new(&Expr::parse(s), ParameterRelation::Exact)
+}
+
+#[test]
+fn identity_and_zero_explain_expansion() {
+    let compare = |f: &FieldCertificate, g: &FieldCertificate| compare(f, g, &BTreeSet::new());
+    let identity = compare(&field("n+m-m-n*m"), &field("n-n*m")).forward;
+    assert_eq!(identity.to_string(), "Yes: f ≡ g after expansion");
+    let zero = compare(&field("0"), &field("n-m")).forward;
+    assert_eq!(zero.to_string(), "Yes: f ≡ 0 after expansion");
+    assert_eq!(
+        serde_json::to_value(identity).unwrap()["certificate"],
+        json!({"kind":"identity"})
+    );
+    assert_eq!(
+        serde_json::to_value(zero).unwrap()["certificate"],
+        json!({"kind":"zero"})
+    );
+}
+
+#[test]
+fn newton_explains_positive_hull_weights() {
+    let compare = |f: &FieldCertificate, g: &FieldCertificate| compare(f, g, &BTreeSet::new());
+    let direction = compare(&field("n*m"), &field("n^2+m^2")).forward;
+    let text = direction.to_string();
+    assert!(text.contains("every monomial of f⁺ lies in the Newton hull of g⁺"));
+    assert!(text.contains("1/2·("));
+    let json = serde_json::to_value(direction).unwrap();
+    assert_eq!(json["certificate"]["kind"], "newton");
+    assert_eq!(json["certificate"].as_object().unwrap().len(), 2);
+    assert_eq!(
+        json["certificate"]["coverage"][0]["weights"][0]["weight"],
+        "1/2"
+    );
+    assert!(json["certificate"]["coverage"][0]["exponent"].is_object());
+}
+
+#[test]
+fn witness_shows_integer_curve_and_exact_leading_terms() {
+    let witness = Witness {
+        curve: BTreeMap::from([
+            (Symbol::new("num_edges").unwrap(), (2u8.into(), 0u8.into())),
+            (
+                Symbol::new("num_vertices").unwrap(),
+                (2u8.into(), 1u8.into()),
+            ),
+        ]),
+        numerator: BTreeMap::from([(6u8.into(), BigRational::from_integer(64.into()))]),
+        denominator: BTreeMap::from([(2u8.into(), BigRational::from_integer(4.into()))]),
+    };
+    assert_eq!(
+        witness.to_string(),
+        "num_edges = 2, num_vertices = 2·t; f ~ 64·t^6, g ~ 4·t^2; f/g → ∞"
+    );
+    let json = serde_json::to_value(&witness).unwrap();
+    assert_eq!(json["curve"]["num_vertices"]["exponent"], "1");
+    assert_eq!(json["numerator"][0]["coefficient"], "64");
+    let zero = Witness {
+        denominator: BTreeMap::new(),
+        ..witness
+    };
+    assert!(zero.to_string().contains("g ≡ 0"));
+}
+
+#[test]
+fn unknown_and_field_certificates_use_typed_reasons() {
+    let unknown = Direction::Unknown(Reason::Validity);
+    assert_eq!(
+        unknown.to_string(),
+        "Unknown: missing obligation: Newton coverage fails; no regular witness found positive for every batch certificate"
+    );
+    let json = serde_json::to_value(unknown).unwrap();
+    assert_eq!(json["missing_obligation"]["kind"], "validity");
+    for reason in [
+        Reason::NotPolynomial("log(n)".into()),
+        Reason::MissingField,
+        Reason::ResourceLimit("too large"),
+    ] {
+        assert!(!reason.to_string().is_empty());
+        assert!(serde_json::to_value(&reason).unwrap()["kind"].is_string());
+    }
+    let upper = FieldCertificate::new(&Expr::parse("n"), ParameterRelation::UpperBound);
+    assert_eq!(upper.to_string(), "<= n");
+    assert_eq!(field("n").to_string(), "= n");
+    let missing = field("log(n)");
+    assert!(missing
+        .to_string()
+        .starts_with("unavailable: not polynomial"));
+    let json = serde_json::to_value(&missing).unwrap();
+    assert_eq!(json["accuracy"]["reason"]["kind"], "not_polynomial");
+    assert_eq!(
+        serde_json::to_value(&upper).unwrap()["accuracy"]["kind"],
+        "upper_bound"
+    );
+    assert_eq!(Verdict::Incomparable.to_string(), "Incomparable");
+}
+
+#[test]
+fn signed_coverage_and_regular_refutations_serialize_as_single_directions() {
+    let c = compare(&field("n"), &field("n*(n-1)/2-m"), &BTreeSet::new());
+    assert!(c.forward.to_string().contains("n ≤ 1·(n^2)"));
+    let json = serde_json::to_value(&c).unwrap();
+    assert_eq!(json.as_object().unwrap().len(), 2);
+    assert_eq!(json["forward"]["certificate"]["kind"], "newton");
+    let c = compare(&field("n"), &field("n^2"), &BTreeSet::new());
+    assert!(c
+        .reverse
+        .to_string()
+        .contains("regular and positive across the batch"));
+    let json = serde_json::to_value(c).unwrap();
+    assert_eq!(json["forward"]["certificate"]["kind"], "newton");
+    assert_eq!(json["reverse"]["certificate"]["kind"], "witness");
+}
diff --git a/src/unit_tests/polynomial.rs b/src/unit_tests/polynomial.rs
new file mode 100644
index 000000000..96ed6a618
--- /dev/null
+++ b/src/unit_tests/polynomial.rs
@@ -0,0 +1,107 @@
+use super::*;
+
+fn poly(s: &str) -> Poly {
+    Poly::from_expr(&Expr::parse(s)).unwrap()
+}
+
+#[test]
+fn canonical_terms_remove_zero_powers_and_combine_constant_terms() {
+    let n = Symbol::new("n").unwrap();
+    let p = Poly::from_terms([
+        (
+            Monomial::from([(n, BigUint::zero())]),
+            BigRational::from_integer(2.into()),
+        ),
+        (Monomial::new(), BigRational::from_integer(3.into())),
+    ]);
+    assert_eq!(p, Poly::constant(BigRational::from_integer(5.into())));
+    assert!(p.variables().is_empty());
+    assert_eq!(p.substitute(&BTreeMap::new()), Some(p.clone()));
+}
+
+#[test]
+fn native_substitution_expands_signed_formulas_and_reports_missing_inputs() {
+    let p = poly("n^2+n*m-m^2");
+    let replacements = BTreeMap::from([
+        (Symbol::new("n").unwrap(), poly("a+b")),
+        (Symbol::new("m").unwrap(), poly("a-b")),
+    ]);
+    assert_eq!(p.substitute(&replacements), Some(poly("a^2+4*a*b-b^2")));
+    assert!(p.substitute(&BTreeMap::new()).is_none());
+    assert_eq!(
+        Poly::zero().substitute(&BTreeMap::new()),
+        Some(Poly::zero())
+    );
+}
+
+#[test]
+fn sparse_arithmetic_preserves_exact_coefficients_and_hull_signs() {
+    assert_eq!(
+        poly("n/2+m/3+1").mul(&poly("n/5-m/7")),
+        poly("n^2/10-n*m/210+n/5-m^2/21-m/7")
+    );
+    assert_eq!(
+        poly("n-1").pow(&5u8.into()),
+        poly("n^5-5*n^4+10*n^3-10*n^2+5*n-1")
+    );
+    assert_eq!(poly("n-1").pow(&0u8.into()), Poly::one());
+    assert_eq!(poly("n-1").add(&poly("1-n")), Poly::zero());
+    assert_eq!(poly("n-m-1").hull(|m| m.is_empty()), poly("n-1"));
+    assert_eq!(poly("n-m-1").positive_hull(), poly("n"));
+    assert_eq!(
+        pow_rational(BigRational::new(3.into(), 2.into()), &(-5).into()),
+        BigRational::new(32.into(), 243.into())
+    );
+    assert_eq!(
+        pow_rational(BigRational::new(3.into(), 2.into()), &0.into()),
+        BigRational::one()
+    );
+}
+
+#[test]
+fn multivariate_powers_match_signed_multinomial_coefficients() {
+    let factorial = |n: u64| (1..=n).product::<u64>();
+    let n = Symbol::new("n").unwrap();
+    let m = Symbol::new("m").unwrap();
+    let expected = Poly::from_terms((0..=8u64).flat_map(|a| {
+        let n = n.clone();
+        let m = m.clone();
+        (0..=8 - a).map(move |b| {
+            let coefficient =
+                BigInt::from(factorial(8) / (factorial(a) * factorial(b) * factorial(8 - a - b)));
+            (
+                Monomial::from([(n.clone(), a.into()), (m.clone(), b.into())]),
+                BigRational::from_integer(if b % 2 == 0 {
+                    coefficient
+                } else {
+                    -coefficient
+                }),
+            )
+        })
+    }));
+    assert_eq!(poly("(n-m+1)^8"), expected);
+    assert_eq!(
+        poly("n^18446744073709551616+m").mul(&poly("n+m")),
+        poly("n^18446744073709551617+m*n^18446744073709551616+n*m+m^2")
+    );
+    assert_eq!(
+        poly("n^1000+m^1000").mul(&poly("n^1000-m^1000")),
+        poly("n^2000-m^2000")
+    );
+}
+
+#[test]
+fn polynomial_conversion_rejects_unsupported_functions_and_exponents() {
+    for expression in ["n/m", "sqrt(n)", "2^n", "log(n)", "exp(n)", "factorial(n)"] {
+        assert!(
+            Poly::from_expr(&Expr::parse(expression)).is_none(),
+            "{expression}"
+        );
+    }
+    assert_eq!(poly("(n+m)^2/2"), poly("n^2/2+n*m+m^2/2"));
+    assert_eq!(
+        poly("2^-3"),
+        Poly::constant(BigRational::new(1.into(), 8.into()))
+    );
+    assert!(Poly::from_expr(&Expr::pow(Expr::integer(0), Expr::integer(-1))).is_none());
+}
diff --git a/src/unit_tests/reduction_graph.rs b/src/unit_tests/reduction_graph.rs
index 43736f83a..caa9d2744 100644
--- a/src/unit_tests/reduction_graph.rs
+++ b/src/unit_tests/reduction_graph.rs
@@ -11,6 +11,58 @@ use crate::types::ProblemParameters;
 use crate::variant::{K3, KN};
 use std::collections::BTreeMap;
 
+#[test]
+fn real_graph_path_comparison_runs_from_registered_formulas() {
+    use crate::poly_compare::{compare_all, compare_profiles, Verdict};
+    let graph = crate::rules::ReductionGraph::new();
+    let paths = graph.find_paths_up_to(
+        "MaximumIndependentSet",
+        &graph.variants_for("MaximumIndependentSet")[0],
+        "QUBO",
+        &graph.variants_for("QUBO")[0],
+        4,
+    );
+    assert!(!paths.is_empty());
+    let profiles: Vec<_> = paths
+        .iter()
+        .map(|p| graph.path_polynomial_profile(p).unwrap())
+        .collect();
+    for profile in &profiles {
+        assert!(!profile.domain.is_empty());
+        assert_eq!(
+            compare_profiles(profile, profile).verdict,
+            Verdict::Equivalent
+        );
+    }
+    let result = compare_all(&profiles);
+    assert!(!result.front.is_empty());
+    // Front comparisons must use the same full batch, not standalone two-path scopes.
+    for (i, j, c) in &result.pairs {
+        if result.front.contains(i) && result.front.contains(j) {
+            assert!(!matches!(c.verdict, Verdict::Dominated { .. }));
+        }
+    }
+}
+
+#[test]
+fn exported_nodes_include_the_full_source_parameter_domain() {
+    let graph = ReductionGraph::new().to_json_value().unwrap();
+    let node = graph["nodes"]
+        .as_array()
+        .unwrap()
+        .iter()
+        .find(|node| node["name"] == "MaximumIndependentSet")
+        .unwrap();
+    let mut names: Vec<_> = node["parameter_names"]
+        .as_array()
+        .unwrap()
+        .iter()
+        .map(|name| name.as_str().unwrap())
+        .collect();
+    names.sort_unstable();
+    assert_eq!(names, ["num_edges", "num_vertices"]);
+}
+
 #[test]
 fn domination_rows_keep_unit_coefficients_on_high_degree_simple_graphs() {
     let source = MinimumDominatingSet::new(SimpleGraph::star(9), vec![1_i64; 9]);
diff --git a/src/unit_tests/rules/graph.rs b/src/unit_tests/rules/graph.rs
index a2a8912d6..c2cb4a0d3 100644
--- a/src/unit_tests/rules/graph.rs
+++ b/src/unit_tests/rules/graph.rs
@@ -1295,6 +1295,39 @@ fn test_to_json() {
     assert!(vc_to_is, "Should have VC -> IS edge");
 }
 
+#[test]
+fn graph_export_identifies_declared_defaults_and_catalog_aliases() {
+    let graph = ReductionGraph::new();
+    let export = graph.to_json_value().unwrap();
+    let nodes = export["nodes"].as_array().unwrap();
+    for problem in crate::registry::problem_types() {
+        let family: Vec<_> = nodes
+            .iter()
+            .filter(|n| n["name"] == problem.canonical_name)
+            .collect();
+        if family.is_empty() {
+            continue;
+        }
+        let defaults: Vec<_> = family.iter().filter(|n| n["default"] == true).collect();
+        assert_eq!(defaults.len(), 1, "{}", problem.canonical_name);
+        assert_eq!(
+            defaults[0]["variant"],
+            serde_json::to_value(graph.default_variant_for(problem.canonical_name).unwrap())
+                .unwrap()
+        );
+        for alias in problem.aliases {
+            assert!(export["aliases"][problem.canonical_name]
+                .as_array()
+                .unwrap()
+                .contains(&serde_json::json!(alias)));
+        }
+    }
+    assert!(export["aliases"]["KSatisfiability"]
+        .as_array()
+        .unwrap()
+        .contains(&serde_json::json!("3SAT")));
+}
+
 #[test]
 fn test_to_json_string() {
     let graph = ReductionGraph::new();
diff --git a/src/unit_tests/truth_table.rs b/src/unit_tests/truth_table.rs
deleted file mode 100644
index dec8b6998..000000000
--- a/src/unit_tests/truth_table.rs
+++ /dev/null
@@ -1,225 +0,0 @@
-use super::*;
-
-#[test]
-fn persisted_tables_validate_row_counts() {
-    for (num_inputs, outputs) in [
-        (2, vec![false]),
-        (usize::BITS as usize - 1, vec![]),
-        (usize::BITS as usize, vec![]),
-        (usize::MAX, vec![]),
-    ] {
-        assert!(serde_json::from_value::<TruthTable>(
-            serde_json::json!({"num_inputs": num_inputs, "outputs": outputs})
-        )
-        .is_err());
-    }
-    let table: TruthTable =
-        serde_json::from_value(serde_json::json!({"num_inputs": 0, "outputs": [true]})).unwrap();
-    assert_eq!(table.num_rows(), 1);
-    assert!(table.evaluate(&[]));
-}
-
-#[test]
-#[should_panic(expected = "representing truth-table rows")]
-fn function_tables_reject_unrepresentable_rows() {
-    TruthTable::from_function(usize::BITS as usize, |_| false);
-}
-
-#[test]
-#[should_panic(expected = "representing truth-table rows")]
-fn output_tables_reject_unrepresentable_rows() {
-    TruthTable::from_outputs(usize::BITS as usize, vec![]);
-}
-
-#[test]
-fn test_and_gate() {
-    let and = TruthTable::and(2);
-    assert!(!and.evaluate(&[false, false]));
-    assert!(!and.evaluate(&[true, false]));
-    assert!(!and.evaluate(&[false, true]));
-    assert!(and.evaluate(&[true, true]));
-}
-
-#[test]
-fn test_or_gate() {
-    let or = TruthTable::or(2);
-    assert!(!or.evaluate(&[false, false]));
-    assert!(or.evaluate(&[true, false]));
-    assert!(or.evaluate(&[false, true]));
-    assert!(or.evaluate(&[true, true]));
-}
-
-#[test]
-fn test_not_gate() {
-    let not = TruthTable::not();
-    assert!(not.evaluate(&[false]));
-    assert!(!not.evaluate(&[true]));
-}
-
-#[test]
-fn test_xor_gate() {
-    let xor = TruthTable::xor(2);
-    assert!(!xor.evaluate(&[false, false]));
-    assert!(xor.evaluate(&[true, false]));
-    assert!(xor.evaluate(&[false, true]));
-    assert!(!xor.evaluate(&[true, true]));
-}
-
-#[test]
-fn test_nand_gate() {
-    let nand = TruthTable::nand(2);
-    assert!(nand.evaluate(&[false, false]));
-    assert!(nand.evaluate(&[true, false]));
-    assert!(nand.evaluate(&[false, true]));
-    assert!(!nand.evaluate(&[true, true]));
-}
-
-#[test]
-fn test_implies() {
-    let imp = TruthTable::implies();
-    assert!(imp.evaluate(&[false, false])); // F -> F = T
-    assert!(imp.evaluate(&[false, true])); // F -> T = T
-    assert!(!imp.evaluate(&[true, false])); // T -> F = F
-    assert!(imp.evaluate(&[true, true])); // T -> T = T
-}
-
-#[test]
-fn test_from_function() {
-    let majority = TruthTable::from_function(3, |input| input.iter().filter(|&&b| b).count() >= 2);
-    assert!(!majority.evaluate(&[false, false, false]));
-    assert!(!majority.evaluate(&[true, false, false]));
-    assert!(majority.evaluate(&[true, true, false]));
-    assert!(majority.evaluate(&[true, true, true]));
-}
-
-#[test]
-fn test_evaluate_config() {
-    let and = TruthTable::and(2);
-    assert!(!and.evaluate_config(&[0, 0]));
-    assert!(!and.evaluate_config(&[1, 0]));
-    assert!(and.evaluate_config(&[1, 1]));
-}
-
-#[test]
-fn test_satisfiable() {
-    let or = TruthTable::or(2);
-    assert!(or.is_satisfiable());
-
-    let contradiction = TruthTable::from_outputs(2, vec![false, false, false, false]);
-    assert!(!contradiction.is_satisfiable());
-    assert!(contradiction.is_contradiction());
-}
-
-#[test]
-fn test_tautology() {
-    let tautology = TruthTable::from_outputs(2, vec![true, true, true, true]);
-    assert!(tautology.is_tautology());
-
-    let or = TruthTable::or(2);
-    assert!(!or.is_tautology());
-}
-
-#[test]
-fn test_satisfying_assignments() {
-    let xor = TruthTable::xor(2);
-    let sat = xor.satisfying_assignments();
-    assert_eq!(sat.len(), 2);
-    assert!(sat.contains(&vec![true, false]));
-    assert!(sat.contains(&vec![false, true]));
-}
-
-#[test]
-fn test_count() {
-    let and = TruthTable::and(2);
-    assert_eq!(and.count_ones(), 1);
-    assert_eq!(and.count_zeros(), 3);
-}
-
-#[test]
-fn test_index_to_input() {
-    let tt = TruthTable::and(3);
-    assert_eq!(tt.index_to_input(0), vec![false, false, false]);
-    assert_eq!(tt.index_to_input(1), vec![true, false, false]);
-    assert_eq!(tt.index_to_input(7), vec![true, true, true]);
-}
-
-#[test]
-fn test_outputs_vec() {
-    let and = TruthTable::and(2);
-    assert_eq!(and.outputs_vec(), vec![false, false, false, true]);
-}
-
-#[test]
-fn test_and_with() {
-    let a = TruthTable::from_outputs(1, vec![false, true]);
-    let b = TruthTable::from_outputs(1, vec![true, false]);
-    let result = a.and_with(&b);
-    assert_eq!(result.outputs_vec(), vec![false, false]);
-}
-
-#[test]
-fn test_or_with() {
-    let a = TruthTable::from_outputs(1, vec![false, true]);
-    let b = TruthTable::from_outputs(1, vec![true, false]);
-    let result = a.or_with(&b);
-    assert_eq!(result.outputs_vec(), vec![true, true]);
-}
-
-#[test]
-fn test_negate() {
-    let and = TruthTable::and(2);
-    let nand = and.negate();
-    assert_eq!(nand.outputs_vec(), vec![true, true, true, false]);
-}
-
-#[test]
-fn test_num_rows() {
-    let tt = TruthTable::and(3);
-    assert_eq!(tt.num_rows(), 8);
-}
-
-#[test]
-fn test_3_input_and() {
-    let and3 = TruthTable::and(3);
-    assert!(!and3.evaluate(&[true, true, false]));
-    assert!(and3.evaluate(&[true, true, true]));
-}
-
-#[test]
-fn test_xnor() {
-    let xnor = TruthTable::xnor(2);
-    assert!(xnor.evaluate(&[false, false]));
-    assert!(!xnor.evaluate(&[true, false]));
-    assert!(!xnor.evaluate(&[false, true]));
-    assert!(xnor.evaluate(&[true, true]));
-}
-
-#[test]
-fn test_nor() {
-    let nor = TruthTable::nor(2);
-    assert!(nor.evaluate(&[false, false]));
-    assert!(!nor.evaluate(&[true, false]));
-    assert!(!nor.evaluate(&[false, true]));
-    assert!(!nor.evaluate(&[true, true]));
-}
-
-#[test]
-fn test_serialization() {
-    let and = TruthTable::and(2);
-    let json = serde_json::to_string(&and).unwrap();
-    let deserialized: TruthTable = serde_json::from_str(&json).unwrap();
-    assert_eq!(and, deserialized);
-}
-
-#[test]
-fn test_outputs() {
-    let and = TruthTable::and(2);
-    let outputs = and.outputs();
-    assert_eq!(outputs.len(), 4);
-}
-
-#[test]
-fn test_num_inputs() {
-    let and = TruthTable::and(3);
-    assert_eq!(and.num_inputs(), 3);
-}
diff --git a/src/unit_tests/unitdiskmapping_algorithms/common.rs b/src/unit_tests/unitdiskmapping_algorithms/common.rs
index a0de7b6be..601d0cc46 100644
--- a/src/unit_tests/unitdiskmapping_algorithms/common.rs
+++ b/src/unit_tests/unitdiskmapping_algorithms/common.rs
@@ -58,16 +58,7 @@ pub fn solve_mis_config(num_vertices: usize, edges: &[(usize, usize)]) -> Vec<us
         .collect()
 }
 
-/// Solve MIS on a Grid using ILPSolver (unweighted).
-#[allow(dead_code)]
-pub fn solve_grid_mis(result: &MappingResult) -> usize {
-    let edges = result.edges();
-    let num_vertices = result.positions.len();
-    solve_mis(num_vertices, &edges)
-}
-
 /// Solve weighted MIS on a Grid using ILPSolver.
-#[allow(dead_code)]
 pub fn solve_weighted_grid_mis(result: &MappingResult) -> usize {
     let edges = result.edges();
     let num_vertices = result.positions.len();
@@ -97,7 +88,6 @@ pub fn solve_weighted_mis(num_vertices: usize, edges: &[(usize, usize)], weights
 }
 
 /// Solve weighted MIS and return the binary configuration.
-#[allow(dead_code)]
 pub fn solve_weighted_mis_config(
     num_vertices: usize,
     edges: &[(usize, usize)],
diff --git a/tests/suites/reductions.rs b/tests/suites/reductions.rs
index 4ec221377..03a030df5 100644
--- a/tests/suites/reductions.rs
+++ b/tests/suites/reductions.rs
@@ -522,9 +522,6 @@ mod topology_tests {
     }
 }
 
-// TruthTable integration tests removed (module is now pub(crate));
-// equivalent coverage exists in src/unit_tests/truth_table.rs
-
 /// Tests for QUBO reductions against ground truth JSON.
 mod qubo_reductions {
     use super::*;
diff --git a/tsconfig.json b/tsconfig.json
new file mode 100644
index 000000000..6c0b32603
--- /dev/null
+++ b/tsconfig.json
@@ -0,0 +1,20 @@
+{
+  "compilerOptions": {
+    "target": "ES2022",
+    "module": "ESNext",
+    "moduleResolution": "Bundler",
+    "lib": ["ES2022", "DOM", "DOM.Iterable"],
+    "types": [],
+    "strict": true,
+    "noEmit": true,
+    "isolatedModules": true,
+    "verbatimModuleSyntax": true,
+    "noUncheckedIndexedAccess": true,
+    "exactOptionalPropertyTypes": true,
+    "noImplicitOverride": true,
+    "noFallthroughCasesInSwitch": true,
+    "forceConsistentCasingInFileNames": true,
+    "allowImportingTsExtensions": true
+  },
+  "include": ["docs/website/src/**/*.ts", "docs/website/src/**/*.mts"]
+}