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test(research): independently audit the coupled-carrier packing cap - #3153
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Answers a bounded part of PR #3153's smaller-replica handoff, with PR #3148's coupled inventory fixed. In the inherited source-window model a cap-attaining packing needs one width-eight role in every capacity-eight bin, taken from a call inside that bin's window. At T20, stage-major order has 11,583 eligible roles for 13,440 such bins and replica-major order 5,940, forcing at least 1,857 and 7,500 non-tight bins. Written Hall-count proofs give 78T+297 and 375T for every positive T, also under replica permutations within complete stage or replica blocks. In the inherited packing dual each non-tight capacity-eight bin costs more than 3/250, so both orders push the complete moment above one at the cap bracket's left endpoint. The shipped interleaved T74 order passes the same necessary matching for all 49,728 bins. Conditional on the pinned inventory, window model, additive bin pricing and inherited local paid profile; arbitrary interleaved T20 orders, a full allocation and native or physical admission remain open. No new kappa. Adds research/coupled-t20-window-audit/ only. Submitted by @commdata2338 with substantial AI assistance (OpenAI Codex research and implementation; packaged with Claude Code). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG
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Summary
Adds
research/coupled-cap-independent/. No discrepancy was found in PR3148's 145-row exchange. The actual T74-to-T740 root gain is strictly positive and agrees with the reported approximately1.4052734766776475e-9improvement. All 2,551 patterns are certified, with 12 tight patterns, and every literal bin is tight. This rules out further packing-only gains for the supplied fixed profile/inventory, not other words or interfaces.Audited head:
f2927a4b8afcf0701a6b945e14f30de1d94f5176. Base main:997e6a9ca7b4f95d50e366f61412fd640d72a88a, priority revision 6. Canonical claim and finding.Credit Jeremy Diviney/PR3148 for the construction, dcharb78/PR3133 for the words/inventory/fill, Gonzalo Mier/PR3143 for the comparator, and the retained supplier, allocation and cap lineage. Notices and exact upstream blob identities are preserved. The first commit pins byte-identical data; the second adds the independent audit and reachable-ancestor replay pins.
Evidence
The supplied ordered widths and local paid profile remain inherited inputs. Native operators, producer algebra, the full physical/prefix/outer release, the bit supplier and all-size/analytic obligations are not independently checked here. No new construction, selected-frontier update or independent human/proof-kernel review is claimed. Substantial automated assistance was used in analysis, implementation, local review and writing.
Merge Danger
Door: two-way. New isolated research package only.
Blast radius: research. No shared checker, selected record, frozen predecessor or workflow is changed.