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Conditional κ ≈ 7.7766181e-4: exact-objective free-form final retiming (490 gates, φ −85.9) replacing #337's 52-gate descent on the same word - #340
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…(490 gates) on PR CrocSwap#337's p10b word, kappa ≈ 7.7766181e-4 (draft; verification in progress) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
…d re-pin the manifest Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
The "Verify research artifacts" workflow (make joint-dual-verify) fails on main and on every open pull request since the root Makefile and README changed (AssertionError: Makefile in joint_dual_compose.check_sources). Regenerated with scripts/experiments/pin_joint_dual_sources.py; verify_joint_dual.py and tests/test_joint_reclaim.py pass (16 tests) under Python 3.11. The joint-dual certificates only change in their recorded source-manifest hash. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> (cherry picked from commit a45747d)
This was referenced Oct 10, 2026
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Draft — full strict replay in progress; this will be marked ready with the exact κ and the PASS line once it completes.
What changes versus #337. Nothing before the final stage: the same oriented p10b source, PR327 complex supplier, 480 frame retimings, 120 target groups, 1,241 entrance families, 240 early restorations, 15 terminal sinks and 125 reorderings, reproduced byte-exactly (post-reorder word
f506e89c…). The final concave-descent selection (52 gates, φ −75.37) is replaced by a 490-gate selection (φ −85.89: 335 descents, 53 uphill moves, 102 constructed frames) found by an exact-objective simulated-annealing search over each gate's full legal frame interval (depth-2 meet/join closure of the neighbouring operand frames plus the word's registered frames), with nested chains, fixed endpoints, exact integer operand source spans, G-nondegeneracy with prime witnesses and COPY lifetimes enforced. Every entry is admitted by the unchangedengines/descent2_transform.py; paid calls 47,820 → 47,801, rank mass unchanged (177,855), final wordb1c96e44….Price. Native κ = 388830904643257/(5·10¹⁷) = 7.77661809286514e-4 (bit binds below PR327's cap), +1.57e-8 over #337's 7.77646131e-4 native value; the 8-level prime-threshold bootstrap adds the same ~3e-15 as in #337.
Package
research/p10b-exact-retimeis #337's package withstages/descent2-selection.json,SOURCE.jsonandMANIFEST.jsonchanged (docs updated with the replay numbers at ready time). Prepared by Rohan Arun with Anthropic Claude assistance; all upstream credits (eumemic, DreamingOfClouds, chafreaky, PR327/PR325 authors) retained.🤖 Generated with Claude Code