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Apply merged net-tax and concentrated-log machinery to the complete selected invoice, retaining kappa and all five framework assumptions. Includes independent exact coefficient corroboration and scoped review. Prepared for @CubeJerry with OpenAI Codex assistance.
Retain the original merged-source certificate and add a pinned, fully charged application with independent interval and binomial/Newton verification. No new kappa. Prepared for @CubeJerry with substantial OpenAI Codex assistance.
Bind the sharp-net proof source to the byte-identical retained copy already in this branch's history. Preserve the original JOINT-SOURCE provenance, proof hashes, scientific checks and receipts. Validated metadata, all eight registered commands, committed bytes and modes, and declared source history in a fresh full-history checkout. Prepared with OpenAI Codex assistance.
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Summary
Reduce #6030's sufficient log2-rank from 65,807,000,000,000 to 1,397,200,000,000 (~47.1x), retaining its complete invoice and κ=0.003125804. The original merged-only #4480 application at H=1,449,000,000,000 remains independently reproducible.
The optional example applies the separately verified sharp-net theorem: N<=1937/250000 permits v=366,p=36,h=6400. Against a retuned old-coefficient certificate at H=1,433,600,000,000, the added improvement is exactly 13/512 (2.5390625%). The pending theorem and its proof are explicitly pinned and exported.
Credit #4433/#4480, #5787 and #6109. Base: 7c49fe3; audited #6030 source: 772dd10.
Evidence
Expected: PASS_SELECTED6030_OPTIONAL_SHARP_NET. Eight registered normal/optimized and read-only portable checks pass. Separate interval and binomial/Newton engines verify the coefficient bound and all 38+37 polynomial coefficients. Full completion is charged; preceding-rank controls reject and all 54+4 outer checks pass. Controls detect understated coefficients, wrong root brackets, omitted paid tails and insufficient product/degree.
Limitations and next questions
No new κ. This reduces a sufficient rank exponent, not runtime, and makes no global-optimality claim. Five framework assumptions remain; the huge word and precision schedule are not materialized. Fresh finite constants must be counted. Full-history validation was unavailable in the shallow checkout.
Attribution
@CubeJerry, with substantial OpenAI Codex assistance; predecessor notices retained. Proofs, pins and reviews. No human or proof-kernel acceptance claimed.