An independent exact recheck of a 2-tetrahedron counterexample to Luo's conjectures on Q-theory of closed 3-manifolds (a recheck of a result by others)

Q. Guo (arXiv:2610.13979, 11 Oct 2026, unrefereed; the paper says ChatGPT supplied the idea) gives a 2-tetrahedron, one-vertex triangulation of the lens space L(3,1) that he says refutes Conjectures 1-3 of F. Luo (arXiv:1003.4413) on Haken's normal surface equation, Thurston's gluing equation and the volume maximum on the space of angle structures. This is an independent recheck of a result by others. We claim nothing new, and nothing about the Poincaré conjecture: L(3,1) is not simply connected, so the restricted versions behind Luo's route to it are untouched. What was rechecked (Tier C: exact integer, rational and Groebner-basis computation, with Regina as cross-check). The triangulation (isomorphism signature cMcabbjak, one vertex, edge degrees 2,5,5, H1 = Z/3, pi1 = C3 by two routes, null-homotopic loop edge); the Q-matching data (rank 2, Lemma 3.1, no 3-cluster, for nonnegative, integer or signed Haken solutions); the unsolvability of Thurston's equation (all 8 sign patterns in both orientation conventions); clause (iv), upgraded from numerical to Tier C by an elementary analytic bound (every non-smooth point of the space of angle structures has volume at most 1.52316, while an exact rational smooth point has volume at least 1.58529; 30-digit floats with a rigorous series-tail bound, not interval arithmetic); minimality of two tetrahedra by a Regina enumeration. Guo's quotation of Luo's conjectures and definitions was checked against arXiv:1003.4413v2. Guo's triangulation is not the only one-vertex minimal triangulation of L(3,1); the other was not tested. Audit. A separate AI agent instance (not a human) reproduced the results with its own code (ACCEPT_WITH_CORRECTIONS; corrections applied). Outcome: CONFIRMED as a recheck; Tier A not reached. Limitations. Milnor's single-tetrahedron bound (a side remark only), the geometrization step used to name the other census classes, the published Contemporary Mathematics version of Luo's paper and the remark of Segerman and Tillmann were not verified; interval arithmetic was not used; no Lean; no human audit; the prior-art search was limited. The third-party papers' full texts are not redistributed.