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Exclude neutral-first G20 two-step savings across all native catalogue routes (no new κ) - #6324
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Mister-Meeseeks merged 1 commit intoOct 31, 2026
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Exhaust all 22 neutral first rewrites and 49,865 second intervals. Exact native geometry and concavity cover every finite catalogue path and every exponent in (0,1). Include independent domain, distance, sign, prefix and portable-replay verification. No new kappa. Prepared for @CubeJerry with substantial OpenAI Codex assistance.
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On the final #5708 word, none of the 49,865 second A2 rewrites after any of its 22 neutral first moves lowers the complete local paid-query moment: 49,392 strict losses and 473 attained ties, for every real 0<t<1. Each frame demand may use any finite separately charged path through all 52,624 native edges on 645 frames. The complete first-step census also gives 2,248 strict losses and 22 ties.
New relative to #6290/#6305: neutral-first depth two and the full native catalogue, extending the published directed route table. #5616 supplies related catalogue geometry for a different, scalar-order-preserving problem; its old caller/flow certificate is not transferred.
Base: 2485805.
#5708 source: 829d01f. Individual input Git/SHA256 pins and question-head pins are in SOURCES.json and TASK.json; no pending executable is imported.
Reproduce (CPython 3.12, stdlib):
Expected: PASS_G20_NATIVE_NEUTRAL_TWO_STEP (49865 / 49392 / 473) and PASS_REGISTERED_RESEARCH_PACKAGE.
Executed: six registered commands; normal/optimized full censuses; every 685-column endpoint and final return; independent complete interval scan, geometry, all 416,025 integer distances, 211 sign proofs and prefix-reuse checks. Full-from-start and prefix invoices agree entry by entry. Thirty-six actual corruptions reject. Committed bytes/modes, export integrity and all six read-only Git-free replays pass. Exhaustive deterministic domain, stopped at depth two; no all-depth search claim. Complete remote tree matches tested contents.
No new κ. Correction frames and catalogue are fixed; each demand pays separately. Costly-first compensation, deeper rewrites, new frames and shared/cancelled demands remain open. Ordinary work, uniform native admission, compiler/precision/tape, full caller and all five framework assumptions remain inherited or unrun. No hosted CI, proof-kernel acceptance or complete-history preflight claimed.
By @CubeJerry with substantial OpenAI Codex assistance and separate domain, algebraic and implementation reviews. Credit Ali Romman (#5708/#5616), unpaidmoon (#6290), Nick Petalas (#6305), and retained native/controller lineage. Apache-2.0.
Proof, certificates, exact validation and open questions:
https://github.com/CubeJerry/integer-mult-bounds/tree/8bf188237e74ea14b48c7c2cbb1b4c7e82650da5/research/g20-neutral-two-step-obstruction
Complementary one-contact result with freely moved correction frames (no dependency):
https://github.com/CubeJerry/integer-mult-bounds/tree/b042dc22b99919734d37cf99f5eca432b28b4365/research/g20-one-contact-free-frame