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Determine the original fixed-height direct-flow scalar exponent (no new κ) - #6329
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Mister-Meeseeks merged 2 commits intoOct 31, 2026
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Prepared for @CubeJerry with substantial OpenAI Codex assistance. No new kappa; no physical supplier admission.
…rence Documentation only; mathematical source and executable bytes unchanged. Prepared for @CubeJerry with substantial OpenAI Codex assistance.
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Determine the complete scalar recurrence of #4436 at its original fixed height: L(n)=n^(s*+o(1)), with 0.99738855928<s*<0.99738855931. All root sources, unmatched boundaries, terminal leaves and complements are included. Uniform mixed-layer limits and a positive binomial-series tail certificate close the asymptotic question behind #6118, #6125 and #6128. This is distinct from #4483's changed-height construction.
Base: a7638a4.
Exact source/dependency Git and SHA256 pins: SOURCES.json; provenance and limits: TASK.json.
Reproduce (Python 3.12, stdlib):
Expected:
PASS_DIRECT_FLOW_FULL_LIMIT,PASS_EXACT_COMPLEMENT_SIGNSandPASS_REGISTERED_RESEARCH_PACKAGE.Executed: 26 full-histogram fixtures, 104 power identities, nine coefficient identities, 27 derivative intervals and 512-term exact complement certificates. Controls reject omitted layers, multiplicities, root sources and positive tails, reversed windows and four altered source files. Normal/-O, clean-copy, committed-byte/mode, export and optimized exported replay pass. Separate Decimal/series diagnostics corroborate the constants; a second independent all-rank proof review is preserved in INDEPENDENT_REVIEW.md; the universal claim rests on the written proof. Fixed domains; no random search.
No new κ. No effective onset or induction constants, physical supplier, selected-frontier change or discharged framework assumption. The result concerns this fixed scalar recurrence only. Full-history preflight was not run in the shallow checkout.
By @CubeJerry with substantial OpenAI Codex assistance in construction, separately implemented checks and adversarial review. Credit zxv (#4436/#4483), Ryanson Jonathan (#4459/#4465/#4467), DLamdata (#6118), Nick Petalas (#6125/#6128), Cinna Davis, Stone and retained lineage. No human/proof-kernel acceptance.
Proof, exact pins and limitations: https://github.com/CubeJerry/integer-mult-bounds/tree/26c3384d26a70e6366023c9cc7670e4ca447eee2/research/direct-flow-exponent-gate
Complete remote Git tree matches the tested contribution.