Problem detail · source-aware
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Does real projective 6-space admit a simplicial triangulation with fewer than 45 vertices? This is Question 3.2 of Guyer, Steinerberger and Yang, “An Efficient Triangulation of RP^5”, arXiv:2603.07808 (2026). The question asks for an improvement on their 45-vertex construction, not for the exact minimum number of vertices.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
The manuscript's Computational assistance section: "OpenAI's ChatGPT was used in the computational exploration, in the development of the verification programs, and in preparing this manuscript. The two implementations were developed within the same AI-assisted workflow; their agreement is not external independent validation." Search assistance, code and prose: the assisted tier.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Site-confirmed: both of the author's exact-arithmetic verifiers (anc/verify.py with integer Bareiss elimination and anc/verify_rational.py with rational Gaussian elimination, Python standard library) were replayed here on 6 September 2026 from a clone of cheptil/44-vertex-triangulation at 2c62b31. Both pass: every facet's supporting hyperplane, completeness of the facet list, the antipodal disjoint-star condition, f-vector (44, 938, 7024, 22555, 34936, 25914, 7404), quotient Euler characteristic 1, in about 3.5 seconds; the negative controls (perturbed coordinate, missing facet) fail as they should. Question 3.2 confirmed verbatim in arXiv 2603.07808. The manuscript's "Computational assistance" section discloses ChatGPT's role and says the two verifiers share one workflow, which is why an independent replay was worth doing.
Correctness: unknown · statement fidelity: unaudited · peer review: none
The manuscript gives an explicit centrally symmetric simplicial 7-polytope with 88 integer vertices. Its antipodal boundary quotient is a 44-vertex triangulation of real projective 6-space, with f-vector (44, 938, 7024, 22555, 34936, 25914, 7404). This improves the 45-vertex construction of Guyer, Steinerberger and Yang and gives an affirmative answer to their Question 3.2. Integer coordinates, facet lists and exact-arithmetic verification code accompany the manuscript. No claim that 44 is vertex-minimal is made.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.