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This was referenced Nov 9, 2026
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Change and mathematical scope
Proves the exact-operator assertion
native_all_columnsfor the pinned selected #6030 native layer and complete all-forward caller, for every positive column multiplicity and arbitrary spectator factors. A constrained quadratic Gauss-sum checker verifies full unitary overlap traces, retaining absolute phases without a tableau, distinguished column or dense operator matrix.The source-bound composition covers 2,922 signed native/helper pairs, 208 intrinsic adapters, all 18 forward calls and 16 wrappers, 7,488 raw contacts, the complete 1,024-entry free-Laurent controller, and every whole-job boundary. Exterior scalar coefficients stay outside tensor powers. The 13,444 productive fields and 66,834 paid calls are unchanged.
No new κ. This proves the stated algebraic implication under explicit ideal owned-reset semantics. Selected-rate physical dispatch, allocation/erasure, compiler, precision/tape and analytic recovery remain separate; no selected record changes.
Sources and reproduction
Base:
7c49fe32c55de02c2c873655c804b16e4c3fef0a. SOURCES.json pins all seven live inputs by Git blob and SHA256. Extends the framework of #5442 and the native verification of #5974/#6043, retaining #6635's chart argument. #6546 covers the local word; this adds its assembled-caller algebra. It supplies the endpoint needed by #6878 without importing either unmerged package.Expected:
PASS_SELECTED_NATIVE_TENSOR_CLOSURE,PASS_GAUSS_TRACE, exact recipe-emission hash agreement andPASS_REGISTERED_RESEARCH_PACKAGE.Validation and remaining work
Executed on Python 3.12.14: normal and optimized complete checks, normal and optimized trace tests, full source-compiler recipe regeneration, and committed-byte/source checks. The trace oracle includes 16,933 small quadratic forms and 120 independent dense circuits. Twenty caller/native controls reject phase loss, wrong factor order, tensor-powered exterior signs, faulty adapters, aliases and source drift; ten additional controls exercise the trace grammar. Lead mathematical review and separate forward-Laurent/direct-character checks also passed.
Finite checks authenticate the fixed source identities; PROOF.md supplies the all-column theorem. The next obligation is a fully charged physical dispatcher with owned return and precision contracts, not another local chart census. This is AI-assisted review, not human or proof-kernel acceptance.
Credit
Prepared for @CubeJerry with substantial OpenAI Codex assistance. Credit DreamingOfClouds, David Arias, Cinna Davis, Gareth Davidson, Ali Romman and the native/controller/compiler predecessors identified in the package. Apache-2.0.
Proof, exact pins, controls and open questions.