Completed-core sharing: conditional kappa > 2^-13

[an664]

This adds a reproducible conditional certificate for

[
T(n)=O!\left(n(\log n)^{1-\kappa}\right),\qquad
\kappa=12310001053253/10^{17}=0.00012310001053253>2^{-13}.
]

The construction combines the pinned #117 complex producer with completed-core scratch sharing and a replayed stopped bit construction. The new allocation shares each scratch role only between fully completed cores with orthogonal outer triple labels. An explicit partition of all 2,024 triples into 83 groups of 24 and four groups of eight reduces the complex allocation to 13,187,822 original streams. Each partial group pays its signed complement transform; internal children, copied centers, data operations and scalar/precision charges remain included.

The partition uses the resolvable-packing construction of Zhang and Ge, Journal of Combinatorial Designs 18 (2010), 209-223, DOI 10.1002/jcd.20234. The exact result is about 17.8% above #117's pinned 0.0001044939. A final public check also found #127's coupled conditional 0.00011239534209971 at ca8725485a822769f24c2e4e9b8955b31a42b044; this certificate is 9.5241% above that claim. These are comparisons with specific checkpoints, not a claim about every concurrent submission. The later submission was inspected but its verifier was not replayed here.

research/completed-core-sharing/ contains the proof, exact certificate, source pins and a standalone verifier. It retains the inherited transparent-dirty-core, physical compiler, stopped ordinary-leaf, semantic precision, analytic/prime and recovery interfaces. It does not claim an unconditional multiplication theorem or a new exhaustive execution of the expanded Gaussian tape program.

Validation:

• python3 research/completed-core-sharing/verify.py: passed on the submitted files. All 81 input hashes, pinned Git blobs, construction replays, exact inequalities and four corruption controls passed. The verifier also rejects Python's assertion-disabling optimization mode.
• All repository make verify groups passed. The initial run completed the first five groups, then Apple Clang rejected -fopenmp; the remaining six groups completed with installed GCC 15 and verified Boost headers. Tracked repository files remained unchanged.
• The focused verifier checks input hashes, regenerates the producer and carrier matching, checks actual bit-frame geometry, replays 1,076,483 events over 32,408 formal columns, checks signed partition/complement phases and independently encloses the exact arithmetic. Corruption controls reject invalid orthogonality, a missing scatter, an omitted paid child and an excessive exponent.
• A dedicated CI workflow runs the same focused verifier on Python 3.11 and 3.14.

Credit and retained notices are in the package. This contribution was prepared with substantial OpenAI Codex assistance; the included finite checks are reproducible, not external peer review.

[Mister-Meeseeks]

Thank you @an664. This contribution is now recorded on main in the scoped reconciliation review and contributor credits.

Contribution: Completed-core sharing with separate dirty-restored cores.

Review and limits: Fresh dedicated full replay; signed phase and physical scratch allocation matter. No identification of independent dirty inputs.

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: 530588a019b4a74f09180680c9e3961bf649ec89. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.