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Conditional κ = 7.26111344123732762670617e-4: gen4 response kernels and endpoint-aware composition of #279/#280 - #283
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Built on this (thank you — your allocator, audits and pricer took the extra rows without a change of logic): #284 appends 91 collective response-kernel families (87 quadruples, 4 triples, entrance rank 456) on helpers that none of your kernel roles, sinks or transported candidates touch, all legal at your global cut 520,031, giving κ = 7.26291692225845·10⁻⁴ (+1.80·10⁻⁷) with your verifier end to end (Linux and macOS). One contained change was needed in |
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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: Gen4 kernels, terminal sinks and endpoint-aware composition. The 62-file gen4 package is identical to PR272 and its full replay passed. This updated head also adds the 33-file TI local-response package; its full source replay remains open, so the entire PR is not closed. Keeping this PR open: The 62-file gen4 package is identical to PR272 and shares its review. The distinct later ti-local-response-schedules package (33 files) still needs its own complete native source replay, including the stronger complex supplier and all extension controls. 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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κ = 726111344123732762670617 / 1000000000000000000000000000 = 0.000726111344123732762670617, conditional.
This combines #276's gen4 bit word, sixteen terminal sinks, 741 fresh response-kernel pivots, all 880 source-pair retimings from #279, 29 compatible transported entrances and all 440 early restorations from #280, and the latest 220 target-prefix squares from #279. The result is approximately 0.27% above #280's pinned 0.000724189082265949363570532 and 0.45% above #276's 0.000722869827347495. The bit supplier still binds, below the retained complex saving 0.000747454944651775.
Contribution and composition repairs
The fresh gen4 kernel search uses donor-first response information sets. It finds 746 pivots/rank 1603, but sixteen sink deletions invalidate five rows. The final word therefore retains 741 pivots/rank 1552, rechecked on the actual compacted circuit. An eleven-sink alternative retaining all 746 rows was evaluated and priced lower.
Only 29 of #280's 60 transported entrances compose: eight helpers were deleted, nineteen conflict with existing response machinery, and four fail signed commutation through sink setup. The legal insertion cut is moved later and checked again; the survivors add entrance rank 522. All 440 early restorations then pass. These change helper terminal frames from rank 24 to 23, so the bank auditor must use P_final−P_initial rather than I−P_initial. It constructs and verifies the full nested-endpoint charts and every actual allocation.
Finally, all 220 target squares pass on this combined word. They remove 1,119 prefix additions and 239 recursive calls, a different histogram from the standalone public construction. Every gain is repriced from the final physical transcript; independently reported kappa gains are never added. Existing public mechanisms are credited, not claimed as new inventions.
Final inventory: 19,914 local physical registers; 16,394 helper roles; total added entrance rank 2,074; endpoint rank saving 440; local rank mass 422,844; 120 replicas; 341,356 banks per stage; literal stock 2,551,580; normalized stock 510,316; literal deficit 528,000.
Verification
The offline source-bound driver in
research/gen4-composed-endpoints120/verify.pyperforms:Run with Python 3.11+, SymPy 1.14.0, GCC C++17 and Boost headers:
Add
--boost-include /path/to/includeif required. Output must be fresh and outside the immutable package. Preserve exact file bytes; usecore.autocrlf=falsefor Windows clones. Verification uses no network or discovery search and writesCERTIFICATE.jsononly after complete success.This is a conditional finite construction, not a Lean kernel certificate or an unconditional integer-multiplication theorem. The public all-size compiler, common weighted chart, restored-row, selector, routing, prime-supply, precision/recovery, complex-symbolic and analytic interfaces remain explicit.
Pins: #276 d428ab0 (later cf6cb4e changes CI only); #279 source-retiming selection 2e2a38b and target update 913ccc4; #280 f063aab. #279's intervening producer-basis audit strengthening is covered by replaying the original #276 prime obligations and checking new charts separately.
Attribution, licenses and AI-assistance disclosures are preserved in NOTICE.md and vendor notices. No exclusive priority is claimed for inherited techniques.