Hill-climbed producers for a conditional κ = 4.105106623e-5 bound

[rohanarun]

Under the inherited analytic and fixed finite-alphabet multitape hypotheses,

$$T(n)=O(n(\log n)^{1-\kappa}),\qquad \kappa=\frac{4105106623}{10^{14}}=4.105106623\times10^{-5}>2^{-15}.$$

This conditional exponent saving is approximately 0.10918% above #46 (82012589/(2*10^12)). The bit saving is 4105275149/10^14. These compare asymptotic bounds, not practical running times.

Construction

Pinned adjacent-swap vectors change the summand orders in RaD's total computations. The selected graphs and carrier matchings reduce the local role counts from 36,685 to 36,656 at h23 and from 48,479 to 48,398 at h25: 110 fewer local roles in total. After replication, width W falls from 178,378,409 to 178,168,258.

The original-envelope labels, both fixed I+J bases, copied centers, every paid endpoint correction, reversed data corners with exact recovery of all ten fallbacks, complex layer and balanced assembly are retained from #46. Complete local profiles and accounting are recomputed for the changed graphs and pinned links.

Validation and scope

Full make verify PASSED at research commit bbd2d88fec0485ed5715d994c9cde6a8ac1d3d3a: 191 tests, all five new focused tests, fresh hill-climbed producer/profile replay and independent physical timeline/dirty-basis checks in both dimensions, full inherited 4,073,300-pair data geometry with exact fallback recovery, and 18 historical patch checks. Completed 2026-10-08T15:05:13.167818+00:00; log SHA256 13925a77be211a5d413732d576bee30c703837966d81475819840c14d29ae721. Validation receipt. Follow-up changes are documentation and receipt metadata only.

The optimizer uses floating-point logarithmic weights and SciPy assignment for a first-order objective. The exact certificate validates the selected pinned construction; it does not certify an exact matching optimum. The updated research README distinguishes the numerical search procedure from the exact certificate for its pinned output. The greedy graph search likewise makes no global optimality claim. All inherited analytic and fixed-tape proof obligations remain, and passing finite checks is not formal verification or external expert acceptance of the whole theorem.

make climbed-producers-verify
make verify

Python 3.11+ and a C++ compiler are required. On Linux/GCC the handoff recommends make verify CXX="c++ -include algorithm". The certificate replay uses pinned links and does not require rerunning the SciPy search.

The increment sits on #46 at 71b6c960c89295e952522dd44111df9cfc51ae90. See research/climbed-producers/README.md, its source manifest, pinned swap vectors, links, profiles and exact certificate.

Attribution

Prepared by Rohan Arun with substantial Anthropic Claude assistance. OpenAI Codex replayed the local exact certificate/tests and submitted this PR. Credit Chafik Boukhalfa (#43/#46), RaD / hipotures (#41), icekylinx, James Chang, Dominik Scholz, Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, OpenAI, Harvey–van der Hoeven and all retained predecessor authors, licenses and assistance notices.

[Mister-Meeseeks]

Thank you @rohanarun. This contribution is now recorded on main in the scoped reconciliation review and contributor credits.

Contribution: Climb producer choices with portable source vectors.

Review and limits: Focused producer tests; bounded search, not a globally optimal construction.

The complete original source, proof/research notes, notices and relevant replay/CI evidence are retained through the pinned source archive. The review distinguishes fresh runs, exact-head historical CI and prior integration evidence. Closing this historical PR as reconciled; its obsolete headline does not replace the current selected bound, and draft/retracted claims retain their explicit qualifications.

Reviewed head: 117caf164e3b235ef20188aa2dc1b49617e9255c. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.