[intqwq]

The phase-adapter research now changes the owner/query protocol beyond the retained fixed phase graph. This adds exact arbitrary-input constructions, explicit failed admission gates, and two fresh Lean modules with eight standard-axiom reports. No improvement beyond PR4610's conditional κ = 0.0030217758 is established.

The changed-owner package emits a 128-owner dyadic adapter satisfying A³ = I, with 2,356 scalar operations and tariff 26,632. Its implementation uses no Gaussian oracle, so finite order earns no productive Gaussian credit; the proposed shared-owner split fails. A separate dirty-helper construction returns (x,y+Fx,Fh) exactly, but three paid calls minus its one independent helper reward costs twice the replaced center bill.

The recursive-query package proves an all-input four-shear producer and both row/column split identities. Its honest direct invoice remains 120 heads per row or column query, not eight: the four-shear implementation costs 480 heads versus 240 for the shared pre/post implementation. Actual transported-projector counterexamples also reject the proposed scalar Temperley–Lieb closure. These are scoped negative gates, not a universal lower bound.

A separate evaluator audits Dugongue's PR4703 complementary B/C suppliers: both 632-row arbitrary-input endpoints, independent helpers, scalar frames, actual paid widths and shared maps. The exact upstream optimized replay also completed, including 2,088 B and 2,048 C paid/helper phase pairs in both orientations and corruption controls. Its local improvement still lacks a profitable complete gauged consumer and compiler admission.

Validation and replay:

• The direct aggregate replay and registered metadata/pin check pass from the isolated publication checkout under global Python 3.14. The generic Python 3.12 launcher was not run locally. The aggregate reruns the small exact checks and authenticates the completed full native replay receipt; optional full regeneration is documented separately.
• Two freshly compiled Lean 4.21.0 modules expose eight axiom reports, using only propext, Classical.choice and Quot.sound. Source/log/object/runtime pins and clean-checkout replay instructions are included. The registered Python hook does not compile Lean.
• All 127 publication files pass the committed-byte check. Exact retained-source copies make ordinary offline replay independent of unmerged origin Git objects. The optional full-history preflight could not pass in the shallow repository. No compiler executable, compiled Lean object, solver cache or virtual environment is included.

The entry point is research/kappa-recursive-phase-checkpoint-20261023/README.md. The earlier 29-report round-seven checkpoint is already published in PR4610 and is linked as predecessor evidence, not counted as fresh work here. This PR starts from canonical main b58ad9ef4d4e861b0eaa5dba41742bdc072dca51, priority revision 7, and leaves the selected record unchanged.

Credit PR4610 and the retained Gaussian/helper/query/compiler lineage; Cinna Davis's PR4696, PR4700 and PR4698; and Dugongue's PR4654 and PR4703. Retained source attribution and notices are preserved. Substantial OpenAI Codex assistance; new work is Apache-2.0.

The remaining task is an affordable physical producer/consumer with complete arbitrary-owner restoration and a strict paid recurrence, followed by native, finite-compiler and outer-transfer admission. These scoped Lean identities and finite checks do not prove the full integer-multiplication theorem.