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Multi-cut kernel condensation: 518 entrances, kappa = 7.11029386054035e-4 - #259
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Built on this (thank you for the generic chart audit, which admits more lines than #254's rule): #266 appends 365 twin-pair families at your earliest cut (676,559) to your 518 — 333 disjoint twin pairs found by a census of all helpers live at that cut (319 of them (2, 2) pairs on lines eᵢ − eⱼ), then 32 more from a second census of every response class at twelve cuts (none at the later cuts, no net-positive XOR triple) — giving κ = 7.11421336565136·10⁻⁴ (+0.0551%) with your seven checkers and pricer unchanged. Two platform notes you may want for your own package: |
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Thank you @Dugongue. Your work and attribution are retained in the published 100-PR review, credits and complete original source. Covered: 518 multi-cut response-kernel entrances. Fresh original local replay exposes a platform-dependent physical-transcript hash after equal-rank sorting. Keep that failed reproduction explicit; later variants are not automatic validation of this entire original head. Keeping this PR open: Provide a deterministic ordering/canonical physical transcript or a source-bound supported-platform replay of this original head, preserving every independent checker. The current macOS run fails the expected transcript hash after equal-rank std::sort. The source archive preserves the entire submission; it does not substitute for the remaining execution or review. The batch's machine-readable disposition records this as partial coverage. Reviewed head: |
Original authors and exact source bytes preserved. Source-only intake and all remaining scientific obligations recorded in research/community-efficient2000-audit. No selected frontier change. PRs: #259, #283, #309, #379, #455, #498, #636, #638, #639, #640, #642, #644, #646, #671, #673, #676, #686, #699, #717, #746, #758, #779, #790, #794, #1043, #1060, #1083, #1086, #1147, #1148, #1150, #1154, #1169, #1176, #1183, #1186, #1192, #1195, #1201, #1207, #1218, #1225, #1238, #1286, #1297, #1319, #1407, #1424, #1464, #1485
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Conditional kappa = 142205877210807 / 200000000000000000 = 0.000711029386054035.
This extends the pinned PR249 construction at
96495746c786d6d0339dbb38c7f553d4af3f88ed. It improves the preceding 132-pair result, 0.00071046520063283, by approximately 0.0794%. This is a checked finite construction under the retained public all-size hypotheses, not a claim of an unconditional multiplication theorem or the current leaderboard record.Construction
Instead of restricting cancellation to equal pairs of helper response columns, select several simultaneous zero-response directions. Share donor lifts when their frames form nested chains, replace singular common frames by explicitly checked nondegenerate subframes, and place compatible transformations at four actual cuts in the physical program. Every added basis operation and its inverse is charged.
The resulting construction admits 518 pivot entrances, removes 1344 raw rank units and 27,772 initial compensation reads, and pays 1,542 basis/inverse gates. The literal bank stock is 867,175. COPY sources are checked for immutability throughout every actual COPY/ERASE window; membership in a selected pivot family alone is not an invalidation.
Verification
The portable verifier regenerates the pinned upstream word, compiles seven C++ checkers, emits the modified word from its frozen witness, and checks:
The verifier also requires the generated word hash and all seven mathematical receipts to match the frozen expected results.
Reproduce
From
research/multicut-kernel-condensation, with Python 3.11+, a C++17 GNU compiler and Boost headers installed:Use a new output directory. The default regenerates upstream data from the included pinned sources.
--snapshots-onlyexplicitly records weaker provenance and is not the default. No network or credentials are required during replay.Scope
Retains the public all-size compiler, common weighted chart, restored-row, routing, prime, precision/recovery, complex correctness and analytic interfaces. This package does not independently prove those general interfaces, claim a practical multiplication speedup, or supply Lean certification. Larger cube-redesign experiments are excluded from the claimed exponent.
Original source licenses and attributions are preserved. The package contains source, frozen witnesses, proofs and expected receipts; no executable binaries are included.