bibkey: erewgoldstein2025magic authors: Muhammad Erew and Moshe Goldstein year: 2025 title: ‘Extremizing Measures of Magic on Pure States by Clifford-stabilizer States’ doi: 10.48550/arXiv.2512.19657 claim: The ququint state and Wigner convention are taken from the paper; the constrained direction analysis is left open there. strata_touched:

• D5/S3/Quantum/Magic/QuquintWignerCriticalGeometry license: citation-only triage: anchor

Ququint Critical Geometry

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DOI 10.48550/arXiv.2512.19657, https://arxiv.org/abs/2512.19657 and https://arxiv.org/html/2512.19657v2. Appendix E, equation (E.3a), gives the state (1,1,zeta^3,1,zeta^2)/sqrt(5). Equation (2.16) gives the phase-point convention after renaming the paper’s (p,q) to (q,p). Section 4.4.2, after (4.55), leaves the mana behavior for the constrained variations to the reader; the last row of Table 2 is undetermined.

The saved full text and abstract were read in the preceding implementation attempt and inspected again for this continuation. PR #5657 records the independent source check. The current Lean development certifies the exact geometry and vanishing first variation. QuquintStrictDecrease proves the exact normalized change and strict mana decrease along every nonzero direction in the specified constrained tangent family. This is a local repository result, not a claim that the source paper contains that proof.

This lane does not claim a general solution of mana extremisation, other dimensions, other critical points, that Claim C is the authors’ verbatim conjecture, or global novelty beyond the recorded search.