[petalas]

Summary

This proves a new obstruction for the later G20 capture of helpers {297, 465, 591}, with reinjection before events 6292, 6296 and 6622 on the frozen PR5708 word. The local signed gain is strictly below -13/2 for every 0 <= C <= 0.01, even with free payload delivery and final restoration. Claim type: scoped proof with an exact finite certificate. No new kappa or selected-frontier change.

three shared payload responses
    -> 17 consistent binary equations
    -> removed paid rank <= 13
    -> surrender H8 + H4 + H8
    -> signed gain < -13/2 throughout the stated interval

The new step enforces one common choice of all three payloads. Optimizing their dependence classes separately gives rank 20, which cannot be attained by consistent responses. The parity relaxation's maximum 13 is attained by its explicit witness; native attainment is unclaimed.

This takes the first Open next question in Jerry Chen / CubeJerry's #6117 and extends the joint-dead pair {297, 465} from Matarener's #6113. Existing native semantics and predecessor results are cited premises, not audit targets. Work stopped at this first obstruction, rather than extending the wider triple search planned in the advance CLAIM.

Evidence

• The 14,794-event parity replay partitions 2,846 paid queries into 2,828 fixed nonzero responses, one free rank-one query, and 17 distinct equations.
• Binary elimination checks all 834 basis candidates. A separate span oracle checks every one of the 131,072 equation subsets, including 292 consistent subsets. Both give maximum removed rank 13. The certificate retains 274 implication closures and 31 rank histograms.
• Integer power comparisons prove the uniform tariff inequality. No floating-point acceptance decision is used.
• Five control groups cover erased labels, incompatible separate-class optima, a wrong reinjection read, an understated target debit and inconsistent equations.
• Registered normal and optimized replays pass with warnings as errors. Each registered command was timed locally, respectively 0.148 and 0.149 seconds, on CPython 3.12.15, macOS 27.0.1 arm64. These are check-duration observations, not performance claims.
• Committed bytes, source ancestry, executable modes, official export/input coverage and read-only Git-free normal/optimized exported replay pass at 74b3ae08041f2942e071985b6f05ffeb54c2f3da.

Exact reproduction from the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B research/g20-later-triple-parity-floor/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/g20-later-triple-parity-floor
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/g20-later-triple-parity-floor --check-source-history --check-modes

Other machines may substitute their CPython 3.12 executable. No dependencies beyond the standard library are needed. Expected direct output is PASS_G20_LATER_TRIPLE_PARITY_FLOOR max_rank=13 target_rank=20 loss>13/2 equations=17 subsets=131072 controls=5 no_new_kappa.

Scope and limitations

Only this fixed schedule, complete target surrender, native permutation-linear injected payloads and deletion of identically zero queries are covered. Other replacement times, extra injections, changed words, target splitting and rank reduction of nonzero queries are outside scope. Physical availability is granted to make the negative bound stronger; it is not certified.

The native word, complete caller, supplier admission, all-size compiler and rounded multiplier were not replayed. All five inherited framework assumptions remain. Independent human and formal proof-kernel review are unclaimed.

Sources are pinned to canonical main 7c49fe32c55de02c2c873655c804b16e4c3fef0a. This contribution was produced by Nick Petalas. Credit CubeJerry, Matarener, Dugongue, Ali Romman, ai-nanachi and the retained G20 native/helper/controller/ordinary lineage. Predecessor files and attribution are unchanged. New work is Apache-2.0.

Open next questions

• Can a different later replacement time or an additional injection escape the consistency obstruction? Derive its exact equations and target debit before physical implementation.
• Can another jointly dead triple pass the same optimistic test? Begin with a source-pinned suffix-support calculation. A larger triple census and native delivery remain open.

Related open work

No open PR found in the live inventory studies this frozen G20 triple or its three replacement times. The distinct occupied-bank work in Discussion #5696 changes frame routing, which this result does not cover.

• Audit #4359 BIT row stock and its #4470 atom change (no new κ) #4612 studies stock for a different BIT supplier source. This local G20 capture obstruction does not compute or compare its stock coefficient or saving.

Completion refresh inspected the other 14 open account PRs created since the advance CLAIM: #6380 through #6388 and #6390 through #6394. None studies this frozen G20 triple or computes its fixed-schedule parity maximum. No same-instance numerical disagreement was identified, and no extra computations checked another contribution.

The task overlap helper reported complete remote pagination but sparse local-note coverage; the overlap checks are not a novelty certificate.

CI notes

Both hosted checks, plan and replay (research/g20-later-triple-parity-floor), passed at exact head 74b3ae08041f2942e071985b6f05ffeb54c2f3da in run 41511932366. The completed checks were read once; separate run metadata confirms completed status, success and the matching head. All registered commands also passed locally. Hosted replay certifies execution of the declared finite checks, not independent scientific acceptance or formal proof-kernel review.

Merge danger

Door: two-way. Blast radius: package. Seven new files under research/g20-later-triple-parity-floor/, with opt-in replay; shared code and the selected frontier are unchanged.