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Exclude every common Gaussian-rational product chart for the actual centre0 code - #5130
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Mister-Meeseeks merged 2 commits intoOct 23, 2026
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The source-derived centre0 code in PR5101 fails its natural-coordinate product probe. This package proves that no common Gaussian-rational owner-to-polynomial chart rescues the G/G^T interface, even after identity padding to any power-of-two N>=128 and with an arbitrary invertible Gaussian-rational output map.
The source reconstruction checks every entry of the actual 112x112 code. Its nonzero transpose defect has rank at most14 (independently certified exactly14). A product isotopy over Q(i)[y]/(y^N+1) forces the difference rank to be0, N/2 or N: the algebra splits into exactly two degree-N/2 fields. The written cyclotomic and unit/isotopy proof gives the all-N conclusion; finite checks supply source binding and boundary controls.
This is a scoped obstruction, not a full supplier or universal impossibility. Arbitrary complex charts, independent input charts, address mixing and changed codes remain outside scope. No native normalizer is commuted through the central product, no changed native word is emitted, and no new kappa or selected-frontier change is claimed.
Validation: Python3.12.2 registered normal/-O checks; committed-byte/source-history checks; official12-file export/check; actual read-only Git-free export replay with PATH=/nonexistent, unchanged bytes, and five rejected mutations covering source drift, receipt value/type, wrong restored mode and wrong Gaussian-factor sign. Root's AI-assisted review found no blocker at proof SHA25651cdb5d5ba294f489f556cbbe5dfe9809ae3672c9ec55cf4fa1ce7853b7c44c2; no human or proof-kernel acceptance is claimed.
Credit remains with Cao Yifan/intqwq and the native lineage, Cinna Davis, Dugongue/mdumitrean, Chris R/Clear1nsight, Dillon and the retained predecessors. The elementary unit/isotopy argument is credited through PR5101 to de Groote and Bürgisser–Ikenmeyer. Prepared by JoyboyBrian with substantial OpenAI Codex (Astra) assistance, Apache-2.0.
Claim: #4930 (comment)
Submission checkpoint: canonical main20a1e31bc6009b9b3f4d084bbaadc6350e34fcba and governing guidance unchanged. Complete10:13–10:14UTC coverage311openPRs,4281Discussionrecords,6884HEADnotes; activep2/moving-coordinate investigations remain distinct. Unpublishedwork outsidecoverage.
Hosted validation follow-up: the original plan job failed on the same eight inherited descendant-source-role/onboarding fixture cases reproduced at base20a1; the research replay job was skipped. Exact job logs were read and compared, not counted as successful replays. The fixture repair in PR #5123 is now merged into canonical main. This PR was subsequently merged by upstream; archive/tooling intake does not retroactively turn its failed or skipped hosted jobs into passing scientific validation. The local evidence above retains its stated scope.