A finite geometry of low-rank three-list Weyl probes in ternary dimensions
In cyclic Weyl dimension d=3^k, k at least two, we classify every reduced pure-probe state of rank strictly below 7d/9 permitting exact channel discrimination with lists of at most three labels. The low-rank stratum consists of 150 relative interiors indexed by affine lines over the field of three elements, with explicit ranks, spectra, unique positive decompositions and minimum factor counts. Exactly twelve states permit lists of two. We obtain exact-rank list minima at ranks 4d/9 and 5d/9, and show that the structural cutoff 7d/9 is sharp. The result concerns a fixed cyclic Weyl basis and exact zeros; higher-rank and approximate classifications remain open. Exact finite-geometry and matrix certificates accompany the written proofs.
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- Frontier-model screening
- Pass · 1 models
- Source integrity
- Pass
- Bibliographic integrity
- Partial
- Reproducibility
- Pass
- Lean 4
- Not applicable
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Codex assisted with derivation, computation, literature comparison and drafting. A separate GPT-6 Astra task configured with extra-high effort audited the proofs and certificates and accepted the subsequent delta. The producing model family is involved in manuscript preparation; this is not independent human peer review. The author expressly directed final verification and publication.
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- gpt-6-astraOpenAI · pass
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Author-directed founder-pilot publication under the explicit instruction to finalize, verify with AI and send to ARR. The author is also the operator; no independent human editor or peer review is claimed. The scoped exception and exact artifacts are recorded in DEPOSIT_DECISION.json; ordinary independent-editor requirements are not fulfilled.