Conditional κ = 0.001588602246663212: static44 with selective bit frames

[chafreaky]

This conditional finite witness reaches κ = 0.001588602246663212: +0.08756181% over #541 and +0.07148322% over #542 at the reviewed heads. Newly opened #543 reports the same combined κ as #542, with a stronger bit supplier that is not adopted in this package. Both changed suppliers are reconstructed and physically admitted by the offline verifier.

The bit word combines #541's 60 commuting preloads, #542's 227 zero-response gate deletions, and ten new frame changes. Their local profile delta relative to the sliced preload word is 10(e1 - e3 - e4 + e6), with the same scalar events, helper inventory, retained centers and inverse cleanup. Every frozen move is replayed with exact rational frame checks and a strictly negative outward moment-cost interval. Native and global physical checks give c = 0.001591129919227630331373 using the original conservative bad-class charge.

The complex side takes #541's explicitly local-only static44 appendix through a new literal owner allocation, full local phase replay and finite invoice. Its residual inventory is 56 width-five, 156 width-eight and 292 width-nine helpers. The admitted global profile gives b = 0.001593245593667524834350. The bit side binds the final composition.

Validation: complete cold macOS/Python 3.14 and Linux/Python 3.12 runs; all 728 complex scalar columns in both orientations and 44 pivot-omission controls; all 2,929 local phase edges and 224 endpoint adapters; wrapper, owner and invoice checks; unmodified native bit checkers with 960/1,440 formal columns and 18 bridge controls; six structural and three mutable-source record mutants; all 138,240 bit helper occurrences with 17 parent and 16 hosting mutants; two independent rational moment engines and all 47 strict outer inequalities. Cross-platform word, program, template and phase hashes agree. CI is separate and is not claimed green.

Fresh bit invoice: native payload 101 bits, global prefix 191 bits charged 192, two-level coefficient bound 421 bits charged 512, row bound 18,355. Fresh complex invoice: 7,168 live rows, 7,682 physical rows, deficit 2,560 and 36,288 whole helper occurrences. Both profiles and invoices are bound to their emitted templates.

Reproduce with Python, NumPy, SymPy, C++17 and genuine Boost headers:

python -B research/static44-selective/verify.py --work /absolute/new/output --boost-include /usr/include

The package freezes every recipe and owner selection; no optimizer or network is needed. Source audit checks 146 original bit/static44 files against exact Git blobs and retains all 78 complex dependency files unchanged. Platform receipts are in research/static44-selective-validation/. A dedicated Python 3.11/3.14 workflow runs the full verifier.

This remains a conditional finite witness. The unchanged complex data controller and data-phase certificate are retained; all-size compilation, common-label/mutable-basis realization, restored work, precision/tape and analytic-transfer contracts remain inherited obligations. No unconditional theorem, complete Lean proof, measured runtime gain or κ = 1 is claimed.

Prepared for chafreaky with OpenAI Codex assistance. Credits and original notices are preserved: Dugongue #541 (preloads and static44 local appendix), rohanarun #542 (response slicing), icekylinx #535 (post-center rank-four baseline), the attributed #531/#484 complex lineage, and #493/#503/#510 native bit and hosting lineage. The new contributions are the ten exact-cost frame changes, complete static44 global admission, and the jointly rebuilt composition.

[Mister-Meeseeks]

Thank you @chafreaky. This contribution at 4858bb38da10cd8a1cd25ef85e7c14f4e2b529dd is incorporated in the reviewed family through #588, published in 9594b61.

Combines trace preloads, zero-response slicing and ten specifically certified bit frame changes with a newly admitted static44 complex allocation. Both changed suppliers receive fresh physical replay. Frozen search choices are nominations; exact frame chains, phases, arbitrary-input columns, owner chronology and the full bill establish the finite witness.

Preserved implementation and research:

• research/static44-selective
• research/static44-selective-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.