Chronological donor sharing: 545 entrances, kappa = 0.000711074913688782665281379

[Dugongue]

Conditional kappa = 711074913688782665281379/1000000000000000000000000000 = 0.000711074913688782665281379.

This improves both PR259's0.000711029386054035 and PR265's0.000711032242134072007667807. It is a modest finite-construction improvement under the retained public interfaces, not an unconditional integer-multiplication theorem.

New physical contribution

Select kernels using the actual costs of shared donors through chronological nested frame chains. This produces545 pivot entrances at nine actual cuts, total entrance rank1371, compared with518 at four cuts and rank1344. The deterministic emitter charges every basis gate and inverse, preserves arbitrary dirty inputs, and uses an explicit total ordering to make the transcript reproducible across C++ implementations.

The120-replica bank construction supports any integer total entrance rank and enumerates all9,952,200 helper/replica/stage assignments. The final rank1371 also admits40 replicas; using120 is a uniform layout choice whose larger finite bill is fully included, not a separate exponent gain.

Public work composed and credited

• PR263: its25 published gate retimings, uniquely rebound by actual scalar instruction and exact old basis. All integer source-span, Gram, chronological, COPY and histogram checks are retained.
• PR261/265: fixed prime2^127-1, exact rare density2m^3/q, eight finite ordinary levels and outer backoff10^-24. The native port reproduces PR261's exact constraints and cutoffs before pricing the new word.
• PR249 and the retained source527/five-stage/bank lineage supply the pinned physical starting point.

No projected gains are added: the final emitted histogram, complete bank allocation and finite invoice are priced together.

Verification

Default replay regenerates the pinned upstream source, emits the new word, runs exact retiming and eight C++ checkers, and requires all frozen mathematical receipts to match. Checks cover20,107 local columns forward and inverse;23,627 global columns; all nine-cut prefix relations; all24 COPY windows; exact charts; every bank assignment; the full finite bill; Lucas-Lehmer; two independent rational moment engines; finite cutoff inequalities;47 strict outer constraints and seven margins; and adjacent-point rejection.

Literal stock is2601390, selector charge1882893202800, counted primitive coefficient187960919367543601 (58 bits), and payload bound98 bits. All costs remain charged.

python -m pip install -r research/kernel-descent120/requirements.txt
python research/kernel-descent120/verify.py --output ../kernel-descent120-replay

Requires Python3.11+, SymPy1.14.0, GNU-compatible C++17 and Boost headers; use a new output directory. No network or credentials are required for replay. Original licenses and public attributions are retained.

Scope

Retains all-size compiler, common weighted chart, restored-row/routing, prime supply, precision/recovery, complex correctness and analytic interfaces. No practical runtime gain, full Lean certificate, or global-optimality claim is made. The fixed-prime cutoff argument permits inherited all-size constants above the counted finite coefficient.

[Mister-Meeseeks]

Thank you @Dugongue. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Chronological donor sharing and endpoint banking.

Review and limits: Fresh full native replay passed: prefix relations, chronological donor lifetimes, all-column inverse restoration and complete bank inventory on the emitted word. Inherited all-size interfaces remain conditional.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: 4f849bd0c08787d588d211ef5f5dbe60f32542b2. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.