Conditional kappa 0.001587467473762886: PR541 trace plus sliced R480 frames

[rohanarun]

Conditional kappa =0.001587467473762886, exactly 793733736881443/500000000000000000: +0.0160671% over #541. Fresh local finite physical verification passes; the unchanged cited complex supplier now binds.

This reconstructs Dugongue #541's60 commuting preloads, applies our227-gate observable slice with227 inverse-cleanup removals, then transfers19 frozen frame reductions from our sliced R480 construction. Each transferred frame is matched to its actual gate and checked for containment. Re-minimizing the entire combined word was a losing experiment; the standalone profile deltas do not add. We recount and emit the complete final word.

Local paid profile: {1:1286,2:1319,3:45,4:169,5:1,6:130,8:9}. Full global profile: {1:370368,2:395232,3:12960,4:64032,5:288,6:52800,7:23040,8:2592}. The unchanged literal whole-owner selection hosts138240 residual occurrences.480 width8 helpers,30720 live rows,30729 physical rows and deficit9984 remain.

Two rational engines give bit c =0.001590005077309865651707. Cited #535 complex b =0.001589991533606044174031 binds. Six explicit finite bootstrap levels,47 strict outer inequalities and invalid-parameter/grid controls certify the displayed conditional arithmetic.

Validation: Python3.14 fresh physical replay and Python3.11 full packaged replay pass. This includes720 local scalar columns,960/1440 native formal columns,18 bridge controls, all675 frame Grams, both orientations,10500480 emitted global events,17 parent mutations and16 hosting mutations. Fresh invoice:101-bit native payload below104;191-bit global prefix charged192;421-bit two-level coefficient charged512; row coefficient18355 below20161. Both versions agree on raw records, profile, invoice and kappa. The first3.11 run's floating diagnostic-only mismatch is preserved; exact mathematical comparisons remain enforced.

Offline reproduction, with Python3.11+, NumPy, SymPy, C++17 and Boost:
python -B research/r480-sliced-minimal-frames/verify.py /absolute/new/output --physical --boost-include /usr/include

The complete source dependencies, reconstruction scripts, original notices and receipts are included. A dedicated3.11/3.14 workflow runs the full finite replay; CI is separate and not yet claimed passed. The original standalone candidate and its BASE receipts are preserved without conflating them with this composition.

All inherited all-size compiler, common-label/mutable-source realization, hosting, precision/tape and analytic assumptions remain conditional. The complex535 operator is cited rather than rebuilt. No unconditional theorem, full Lean proof or measured runtime gain is claimed.

Prepared for rohanarun with OpenAI Codex assistance. Credits: Dugongue #541 (unmodified preload constructor and trace refinement, disclosed OpenAI assistance); DreamingOfClouds #510 and eumemic #493 (disclosed Claude assistance); Dylan Crow #370; Zhihao Chen #425; icekylinx #535; #539 and #461/#464/#465 literal-charge ancestry; all original source notices and licenses preserved.

[Mister-Meeseeks]

Thank you @rohanarun. This contribution at fceff375b8308e793afbc684690341fab5affc39 is incorporated in the reviewed family through #588, published in 9594b61.

Observable slicing deletes only exact target-zero A responses and their inverse cleanup. Nineteen causal minimum-frame changes are transferred by exact gate identity to the preloaded word and every containment is rechecked. Least feasible subspace labels for a fixed word are not moment-optimality. Full --physical maintainer replay passed, including native columns, bridge and hosting controls; PR535 complex input is an already reviewed dependency.

Preserved implementation and research:

• research/r480-sliced-minimal-frames

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.