{ "schema_version": "1.0.0", "source": "vibemath", "problem_id": "vibemathed:a-44-vertex-triangulation-of-mathbb-rp-6", "title": "A 44-vertex triangulation of $\\mathbb{RP}^{6}$", "canonical_statement": "Does real projective 6-space admit a simplicial triangulation with fewer\nthan 45 vertices? This is Question 3.2 of Guyer, Steinerberger and Yang,\n“An Efficient Triangulation of RP^5”, arXiv:2603.07808 (2026).\n\nThe question asks for an improvement on their 45-vertex construction,\nnot for the exact minimum number of vertices.", "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.", "current_status": "resolved", "solution_events": [ { "id": "vibemathed:a-44-vertex-triangulation-of-mathbb-rp-6:event", "problem_id": "vibemathed:a-44-vertex-triangulation-of-mathbb-rp-6", "type": "proved", "status": "resolved", "occurred_at": "2026-09-06T00:00:00.000Z", "title": "Alexey M. Kolosov — A 44-vertex triangulation of real projective 6-space", "summary": "The manuscript gives an explicit centrally symmetric simplicial\n7-polytope with 88 integer vertices. Its antipodal boundary quotient\nis a 44-vertex triangulation of real projective 6-space, with f-vector\n(44, 938, 7024, 22555, 34936, 25914, 7404).\n\nThis improves the 45-vertex construction of Guyer, Steinerberger and\nYang and gives an affirmative answer to their Question 3.2. Integer\ncoordinates, facet lists and exact-arithmetic verification code\naccompany the manuscript. No claim that 44 is vertex-minimal is made.", "ai_contribution": "ai_assisted", "attempt_ids": [ "vibemathed:a-44-vertex-triangulation-of-mathbb-rp-6:attempt" ], "method_family_ids": [ "vibemathed:a-44-vertex-triangulation-of-mathbb-rp-6:method" ], "source_assertion_ids": [ "vibemathed:a-44-vertex-triangulation-of-mathbb-rp-6:assertion" ] } ], "attempts": [ { "id": "vibemathed:a-44-vertex-triangulation-of-mathbb-rp-6:attempt", "problem_id": "vibemathed:a-44-vertex-triangulation-of-mathbb-rp-6", "model": "ChatGPT (OpenAI, model version unstated)", "provider": "OpenAI", "attempted_at": "2026-09-06T00:00:00.000Z", "human_collaborators": [ "Alexey M. Kolosov" ], "exposure": "unknown", "prompt_public": null, "outcome": "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.", "failed_routes": [], "artifacts": [ { "label": "44-vertex-triangulation", "url": "https://vibemathed.com/problem/rp5-24-vertex-triangulation", "kind": "other", "license": null } ], "sources": [ { "label": "Alexey M. Kolosov — A 44-vertex triangulation of real projective 6-space", "url": "https://github.com/cheptil/44-vertex-triangulation", "kind": "primary-mathematical-source", "license": null }, { "label": "VibeMathed: A 44-vertex triangulation of $\\mathbb{RP}^{6}$", "url": "https://vibemathed.com/problem/a-44-vertex-triangulation-of-mathbb-rp-6", "kind": "source-assertion", "license": "https://vibemathed.com/data-license" } ], "cost_usd": null, "independence": "unknown" } ], "verifications": [ { "id": "vibemathed:a-44-vertex-triangulation-of-mathbb-rp-6:verification", "problem_id": "vibemathed:a-44-vertex-triangulation-of-mathbb-rp-6", "solution_event_id": "vibemathed:a-44-vertex-triangulation-of-mathbb-rp-6:event", "level": "unreviewed", "mathematical_correctness": "unknown", "statement_fidelity": "unaudited", "peer_review": "none", "verifier": "VibeMathed (source-reported label)", "verified_at": null, "note": "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.", "sources": [ { "label": "VibeMathed: A 44-vertex triangulation of $\\mathbb{RP}^{6}$", "url": "https://vibemathed.com/problem/a-44-vertex-triangulation-of-mathbb-rp-6", "kind": "source-assertion", "license": "https://vibemathed.com/data-license" }, { "label": "Alexey M. Kolosov — A 44-vertex triangulation of real projective 6-space", "url": "https://github.com/cheptil/44-vertex-triangulation", "kind": "primary-mathematical-source", "license": null } ] } ], "sources": [ { "label": "Alexey M. Kolosov — A 44-vertex triangulation of real projective 6-space", "url": "https://github.com/cheptil/44-vertex-triangulation", "kind": "primary-mathematical-source", "license": null }, { "label": "VibeMathed: A 44-vertex triangulation of $\\mathbb{RP}^{6}$", "url": "https://vibemathed.com/problem/a-44-vertex-triangulation-of-mathbb-rp-6", "kind": "source-assertion", "license": "https://vibemathed.com/data-license" } ], "recommended_mode": "verify", "recommended_exposure": "result_only", "opportunity_signals": [ { "id": "vibemathed:a-44-vertex-triangulation-of-mathbb-rp-6:signal:watch_only", "problem_id": "vibemathed:a-44-vertex-triangulation-of-mathbb-rp-6", "kind": "watch_only", "reason": "Current public evidence does not meet the default replay threshold.", "generated_at": "2026-09-13T16:28:40.178Z" } ], "uncertainties": [ "VibeMath has not independently verified the mathematical claim.", "AI-attempt independence and training-data exposure are unknown unless explicitly documented.", "VibeMath has not independently audited the mathematical statement, proof, or novelty claim." ], "generated_at": "2026-09-13T16:28:40.178Z" }