Conditional κ = 0.001592517889315014: eight rank-five kernel pivots

[eumemic]

κ = 0.001592517889315014 (conditional).

This new finite witness is 0.034484749% above the tied #551/#552 value 0.001591968902833346. It promotes eight post-center kernel pivots in pinned #552 from entrance rank four to rank five, then constructs a new chronological whole-owner assignment. Complex b = 0.001595058047790616770328 binds; the cited unchanged #543 bit supplier has c = 0.001653826988146798944268. Concurrent #555 raises bit headroom but does not change this complex-bound minimum.

Two complete four-pivot groups change entrance and kernel frames while retaining every scalar instruction and coefficient. The helper inventory becomes {4:8,5:48,8:156,9:292}. The local profile is {1:2316,2:424,3:464,4:192,5:56,6:56,8:8}. After literal owner admission, the complete paid profile is {1:166880,2:30528,3:35779,4:13824,5:4032,6:4032,7:208,8:576,39:1,48:1660}. These complete profiles are priced; estimated gains are not added. Promoting all 48 eligible pivots loses after packing costs.

The offline verifier reconstructs the pinned #552 provider from primitive inputs and applies the deterministic promotion. It checks all 728 formal columns in both orientations, every arbitrary dirty helper, both reflected paid ledgers, 44 retained and eight new omitted-pivot controls, 11 native controls and normalized wrappers. It recompiles all 2,929 phase edges and 224 endpoint adapters, checks all 36,288 literal helper roles and seven owner corruptions, and derives a fresh finite invoice. Both rational moment engines certify the endpoints and reject adjacent ticks; seven finite bootstrap levels satisfy all 47 strict outer constraints. Four outer and 13 malformed-admission controls reject.

python -B research/complex-rank5-pivots8/verify.py --work /absolute/new/output

Python 3.11+ and NumPy; no network, optimizer, GPU or C++ compiler is needed for replay. Full packaged replay and a separate clean archive replay pass locally. Receipts are retained in research/complex-rank5-pivots8-validation. Dedicated 3.11/3.14 CI is provided; GitHub CI is separate and is not claimed green. The owner list is serialized in asynchronous invocation order, then helper order, matching the unchanged emitter and independent chart-stream auditor. Actual prefix 225 is below charged 512; row coefficient 16,467 is below 20,161.

This is a new branch and new PR. All earlier published heads and claims remain frozen. The construction changes starts/helper widths and repacks owners, so it is outside #557's fixed-boundary/fixed-owner frame ceiling and the analogous independently checked #552 frame-only model.

The numerical claim remains conditional on inherited all-size compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic-transfer contracts. The bit supplier's interleaved source writes retain its stated H1–H5 interface premise. This package cites and exactly reprices #543, rather than claiming a fresh bit rebuild. No unconditional multiplication theorem, complete Lean proof or practical speedup is claimed.

Prepared for eumemic with OpenAI Codex assistance. Credits and original AI disclosures are retained for Dugongue #552/#548/#541; chafreaky #551; rohanarun/Claude #534; icekylinx #535/#531; DreamingOfClouds #484 and the attributed kernel, phase, normalized-wrapper and arithmetic ancestry; eumemic/Claude #543; eumemic/Codex #550's hardened assembly; and lydakis #275's retained finite-frontier method. Source pins, preserved notices/licenses, the exact construction argument and replay receipts accompany the package.

[Mister-Meeseeks]

Thank you @eumemic. This contribution at 060b137c8a6f9d73fd7864c7f8cf2736d6441774 is incorporated in the reviewed family through #588, published in 9594b61.

Eight selected pivots gain rank-five entrances and matching kernel frames without changing scalar operations. Width reduction and the whole-owner reallocation are charged together; promoting all eligible pivots is not assumed favorable. All 728 columns per orientation, kernel omissions, phases, wrappers, owners and exact assembly are checked. Canonical source bytes match the #588 cold-replayed foundation.

Preserved implementation and research:

• research/complex-rank5-pivots8
• research/complex-rank5-pivots8-validation

The family review and individual disposition record the scope, evidence and attribution. Parallel and intermediate contributions remain credited even where a later composition has a stronger bound. The published multiplication bound remains conditional on the documented compiler, realization, hosting and analytic assumptions; these finite checks are not a full Lean multiplication proof.