Verify paired helper-kernel boundaries and their caller limits

[RossRichardson]

Summary

Verify one paired-helper entrance method on three fixed BIT words: ten rank-one R429 entrances, a common-E2 R429 FULL word and a common-E2 R438 hybrid word. The complete local masses are5087,4461 and4539, with every basis ADD, forced public climb, target lift and copied total included.

All ordinary inputs are arbitrary. Public helper cancellation and the clean target shear hold over F2; source/helper restoration and literal inverse are exact over the integers. The signed targets retain nonzero even helper coefficients. Actual rational ADDRESS charts establish each paired residual, with compiler admission left explicit.

Scope and limits

Only research/bit-paired-helper-boundaries is added. Its three literal words are related instances of the same boundary change, not three unrelated searches. The historical selective/mixed-entrance screens and separate B11 partition census are excluded.

The common-E2 words have318/327 width-six helpers and111 width-eight helpers. R438 uses one required-zero private field for nine copied totals (rank sum52) and pays83 target FULL lifts. Exact GL ADDRESS charts exclude primes2,3,5;160 frames have odd projector denominators. Compatibility with a narrower orthogonal/dyadic recursive compiler, paid scalar routes, source/tape access and rounding remain open.

A dedicated-cover helper fixture checks432 ADDRESS columns and36 assignments. Twelve R429 replicas place all5148 helper roles into969 banks, with333 paid rank-four pads. The whole-cover doubled-chart, distinct same-call adapter, full local-footprint and serial-call premises are explicit. It supplies no public pending-window allocation.

For a fixed common nontrivial N and N-independent scalar bank-GL adapters, a written rank argument gives k>=n. Separately, the uniform common-prefix invoice gives D<=111n-k(F+C)<=0 when all111 public ports and every FULL-lift/COPY tariff are charged. Mixed E, port mixing, operator-valued adapters, changed source cuts or changed endpoint credits require another proof. No positive supplier, unrestricted lower bound, selected-frontier update or new κ is claimed.

Test plan

• Complete registered Python3.12.14 replay of five producer stages, two independent checkers and actual-launcher integrity controls at scientific commit 1b2638a3b34ffb7cf6cb5b90e8fd14ca7f216127; final publication adds only review/validation prose and generated-certificate display metadata.
• Independent dense forward/inverse maps: all651/660 ordinary columns, zero-private lifecycles, actual semantic dirty matrices, integer basis inverses and source-to-join binding.
• All434 used frames and1599 distinct MOVE/COPY charts, including complete16-column ADDRESS identities and sufficient prime exclusions.
• Seven leading-prefix cap/COPY vectors, faithful hybrid operators, all5148 role placements, eight caller/owner defect controls and written all-bank/arbitrary-cover proofs.
• All30 frozen inputs and29 explicit path/comparison adapters; complete typed receipts and five complete word/geometry bodies. Mutation, path-collision, missing-coverage and nested poisoned-cache controls pass in normal/-O and optimized scientific-commit export.
• Metadata/source-history preflight passed.
• Automatic exact-head GitHub CI 39249527585 passed at a5ec08800cc9816feb2f43c3880cc90024ee6155, including full replay and unchanged-input gate. No manual rerun requested.

Sources and credit

Scientific pin 20ecf2891d80b5acf18d980b2164fb44ea7faa90. Retain Sagar Thakrar's R438 transport and the eumemic/DreamingOfClouds/Ali Romman E8/BIT ancestry. The R429 source-code word and FULL compensation are prior interfaces in PR3645 and PR4039.

The dedicated cover method credits PR386, Zhihao Chen and Dylan Crow's PR370 ancestry. Compensation-kernel and paired extraction methods credit Yiyang Lu PR2857, its Philippe Van Velzen/Jeremy Kothe lineage, and Jeremy Diviney PR2908. Karl Appel PR369 studies related BIT kernel entries on a different predecessor. No priority or generic-method novelty is claimed.

Prepared by Ross Richardson with substantial OpenAI Codex assistance and separate AI mathematical/integrity reviews. Apache-2.0; original bytes and notices retained. No independent human or formal-kernel certification.