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Rule out profitable first-read captures of any G20 helper subset (no new kappa) - #6117
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Mister-Meeseeks merged 1 commit intoOct 28, 2026
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Prepared for @CubeJerry with substantial OpenAI Codex assistance. No new kappa; fixed PR5708 word and individual first-read schedule only.
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No new κ. On the pinned PR5708 word, first-read capture of any subset of all 415 helpers cannot improve the local BIT moment for 0 <= C <= 0.01, even with arbitrary native-linear payloads and free setup/restoration. Each chosen rank-8 helper incurs a loss greater than (5/128)*4^(1-C); partial-only subsets have gain at most zero.
New evidence: a 108-color flag certificate covers 64,274 tokens, including three cross-helper early queries. The chronological graph-kernel proof closes the fixed-schedule larger-set question left by Matarener's #6113. It differs from Ali Romman's #5604 static entry bound and credits the #5679/#5708 word, ai-nanachi's #5512 and Dugongue's late-binding work.
Base: 721c038 (canonical main rechecked 2026-10-28 11:23 UTC).
Published commit: e5e5141; its complete Git tree matches the tested tree.
Source Git blobs: word 3877a72d8a15adb03f6492f7d2fd8fa902ecb639; frames 9edf8d95b45a9c9c766a956bfcd3c19cf07bc13c; invoice 29cd42b8baa531f2598b9b8894fd514c754ed17c.
Proof, SHA256 pins, certificate, scope and research log.
Reproduce with Python 3.12, standard library only:
python3.12 -B scripts/research_package.py --package research/g20-joint-capture-flag-boundExpected: PASS_G20_ALL_SUBSET_FIRST_READ_FLAG_BOUND.
Executed: normal/isolated optimized replays; independent set/bit-mask rows; opposite-pivot elimination; seven substitution fixtures; eight rejecting controls (missing/duplicate/dependent tokens, both flags, omitted early query, forged rank, damaged source). Certificate regeneration matches decompressed JSON. Committed bytes/modes/source ancestry, replay selection, official export integrity and read-only Git-free normal/optimized replay pass.
Limits: fixed word, coordinate ownership, native permutation-linear payloads and individual first-read schedule only. Later joint-dead captures and changed circuits remain open. No native endpoint, complete caller or recursive supplier replay; no formal proof-kernel review. Inherited framework assumptions remain unchanged. Local claim recorded; Discussion posting unavailable.
Prepared for @CubeJerry with substantial OpenAI Codex assistance. Apache-2.0; predecessor files and selected frontier unchanged.