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Attain exact P104 dyadic spectral correction ranks 832 and 1664 - #6238
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PR6181 leaves exact Gaussian-dyadic attainment of its modular correction bounds open. This contribution constructs one determinant-one common code, using PR3979's explicit P104 triangular congruence, that attains exact correction rank832 for (alpha,beta)=(1,169) and1664 for (13,13). No scratch or division by13 is needed. The proof also gives the requested explicit integral n=2,r=1 witness.
The lower bounds for arbitrary joint codes and identically returned scratch are credited to Nick Petalas/PR6181. The new upper construction uses Chris R / Clear1nsight's stronger explicit congruence, not just the abstract Gram premises.
PROOF.mdstates the ordered identities, rank argument and exact scope.Verification on Windows11 / CPython3.12.11 passes normally and under
-O, with identical complete receipts: six literal endpoint cases (dimensions8 and32), actual104-port source reconstruction, two factored large minors, and eight rejecting controls. The104-port coupling minor has determinant1/8; the832/1664 minors are both nonzero modulo13.CERTIFICATE.jsonandVALIDATION.jsonretain the evidence. Metadata/source pins and committed-byte/source-history checks pass. Separate AI mathematical review found no blocking issue.Limits: endpoint matrix rank is not a native-call tariff. No physical code/correction recipe, ownership/restoration schedule, identity-side completion, complete signed invoice or new kappa is supplied. The full21632-square endpoint remains factored. No hostedCI, independent human or formal-kernel acceptance is claimed. Selected #6030 is unchanged.
Canonical claim. Credit Nick Petalas, Chris R / Clear1nsight and the retained P104/native/caller/compiler lineage. New construction, checker and write-up: AAAmirinu with substantial OpenAI Codex assistance; Apache-2.0.