Extreme-frame retiming on #284's gen4 word: conditional κ = 7.26319877913759e-4 (+0.0039% over #284; below #285)

.github/workflows/gen4-extreme-frame-retiming.yml

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+name: Verify extreme-frame retiming on PR284's gen4 word
+
+on:
+  push:
+    paths:
+      - 'research/gen4-extreme-frame-retiming/**'
+      - '.github/workflows/gen4-extreme-frame-retiming.yml'
+  pull_request:
+    paths:
+      - 'research/gen4-extreme-frame-retiming/**'
+      - '.github/workflows/gen4-extreme-frame-retiming.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  replay:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 60
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7
+        with:
+          python-version: '3.12'
+      - name: Install toolchain and SymPy
+        run: |
+          sudo apt-get update && sudo apt-get install -y g++ libboost-dev
+          python3 -m pip install sympy==1.14.0
+      - name: Check out pinned PR284 separately
+        run: |
+          git init "$RUNNER_TEMP/pr284"
+          git -C "$RUNNER_TEMP/pr284" fetch --depth 1 https://github.com/CrocSwap/integer-mult-bounds.git 2c991a3ac400057059145c837e8b32bba9128346
+          git -C "$RUNNER_TEMP/pr284" checkout --quiet FETCH_HEAD
+      - name: Replay PR284, apply the passes, rerun every native check
+        run: python3 -B research/gen4-extreme-frame-retiming/verify.py --pr284 "$RUNNER_TEMP/pr284/research/gen4-collective-families-283" --output "$RUNNER_TEMP/replay" --cxx g++
+      - name: Require committed files to remain unchanged
+        run: git diff --exit-code

research/gen4-extreme-frame-retiming/LICENSE

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research/gen4-extreme-frame-retiming/MANIFEST.json

@@ -0,0 +1,12 @@
+{
+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "NOTICE.md": "c46b6471b8aa795ba4ebd79e542e914e9bf1b4c8ffe8a3aebed7d14e3e376ad1",
+  "PROOF.md": "e3e7f8cfffbf36db520888ad564a73b462a1af0997262e468ed860629c3e5f91",
+  "README.md": "53c9c9156f942c43282d25f2dfdc9ee79520e7509b194ac88178cc792a9c2847",
+  "code/emit.py": "7f4b6eb07da1ddccc10de1030a231a7f558a3c2386de5e38143ba96d4351b147",
+  "code/frames_audit.py": "5a7b7f43a38a768a59ac1dab9e53dfc5fdeddbc42135cc6d820e557dee74e723",
+  "code/scan.py": "875eb66cbc72929429e30a7de380e280d4eb96f0cd6bdb036c03fa191eb1a925",
+  "data/passes.json": "fa4857d70009a457ee92a7c803c9e33d98ff956d7d56354ff4dc4a726f6330ea",
+  "expected.json": "5dbc0f2f34da3833706fdbb67b0de4f51fd8c3403dbed00d2b4002e13670f469",
+  "verify.py": "75a8b68036d2666a237d9bf8d37116c0259907894ab0ffadedeb64a16e8f258b"
+}

research/gen4-extreme-frame-retiming/NOTICE.md

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+# Notice
+
+This package builds on #284 (chafreaky, `research/gen4-collective-families-283`, commit `2c991a3ac400057059145c837e8b32bba9128346`). It uses #284's verifier and native checkers unchanged, by reference to a separate pinned checkout, and does not copy or modify that package.
+
+#284 extends #283 (Dugongue), which composes work by DreamingOfClouds (#276 gen4 word), rohanarun (#279 retimings and target-prefix squares), utcorvusvolat-dotcom (#280 restorations and entrances), and the earlier lineage they credit. lydakis's #275 zero-frame restores motivated this generalization.
+
+The extreme-frame scan, the exact join/meet construction and the local emitter are new here. Prepared by Joel Pulikkan (GamingPuzzled) with Anthropic Claude assistance; Apache-2.0 (see `LICENSE`).

research/gen4-extreme-frame-retiming/PROOF.md

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+# Why the retimed word is valid
+
+**Input.** #284's final COHORT249 word (SHA256 `29ec9733…b605`), its frames and its pinned final frames, all regenerated by #284's verifier.
+
+**Change.** A pass changes the frame field of selected ADD records (`op = 1`). Operands, scalar, category and order stay the same. For the operand roles of changed gates only, the MOVE records are rebuilt:
+- before each use, one MOVE goes from the role's current frame to the frame that use requires;
+- at the end, one MOVE goes to the role's pinned final frame.
+
+All other records are byte-identical and keep their positions. `emit.py` asserts that the ordered non-MOVE stream equals the input's, with only the selected frame fields replaced.
+
+**Nesting.** For a unit U (an equal-frame ADD component, or a single ADD) and each operand role r:
+- `P_r` is the frame of r's use immediately before U (or r's initial frame);
+- `N_r` is the frame of r's use immediately after U (or r's final frame).
+
+The new frame G satisfies `P_r ⊆ G ⊆ N_r` for every r. `frames_audit.py` checks this with exact integer dot products, so every rebuilt MOVE is a nested, nonnegative-rank jump. #284's independent legality checker confirms it chronologically on the whole word.
+
+**Extremes.**
+- Join passes: `G = Σ_r P_r`, with `dim G` equal to the rank of the union of their bases, and `G ⊆` the old frame.
+- Meet passes: `G = ∩_r N_r`, with `dim G = 24 − rank(stacked annihilators)`, and `G ⊇` the old frame.
+
+Both are checked exactly. Any G between the bounds keeps nesting valid. The extremes are chosen because the price rewards wide children: `r ln r` is convex, so the optimum over the bounded chain sits at an end.
+
+**Scalar correctness.** All changed gates are category 12/28 helper additions. The scalar map is unchanged as a sequence of signed additions; only the frames they run in move. #284's five-stage checker replays every independent physical input column over F2 on the new word, including arbitrary helper dirt, and confirms restoration and all copied-centre work. That is the same acceptance test #284 applies to its own transforms.
+
+**Banks and charts.** #284's bank checker recomputes every exact chart, including the 62 new frames' connectors, and the full role/replica/stage allocation on the new word. Stock is unchanged at 2,549,300 literal (509,860 normalized).
+
+**Price.** Rank mass is unchanged (422,388 local). Calls change only by the histogram deltas in the README. The exact price, finite invoice (58-bit primitive coefficient, 96-bit payload) and fixed-prime assembly (q = 2^127 − 1, eight ordinary levels, 47 strict constraints, adjacent grid point rejected) give κ = 726319877913758986831841/10^27.