{ "schema_version": "1.0.0", "source": "vibemath", "problem_id": "vibemathed:half-collinear-graviton-vertices-as-weighted-root-cone-enumerators", "title": "Matrix-Tree Obstruction for Half-Collinear Graviton Vertices", "canonical_statement": "In the half-collinear single-minus graviton recursion of Guevara, Lupsasca, Skinner, Strominger and Weil, the multipoint vertex weights depend on global cut tests, which blocks a direct matrix-tree formula outside a restricted decay region. The paper's footnote 4 states the obstruction and its conclusion leaves the general simplification to future work. This result identifies those cut tests as exactly positive-flow conditions, making each retarded vertex a weighted enumerator of directed spanning-tree root cones containing a kinematic netflow vector, so the directed Matrix-Tree Theorem applies whenever the feasible trees form a complete arborescence family.", "plain_summary": "VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.", "current_status": "partial", "solution_events": [ { "id": "vibemathed:half-collinear-graviton-vertices-as-weighted-root-cone-enumerators:event", "problem_id": "vibemathed:half-collinear-graviton-vertices-as-weighted-root-cone-enumerators", "type": "proved", "status": "partial", "occurred_at": "2026-08-09T00:00:00.000Z", "title": "Author repository", "summary": "Answers the obstruction rather than the whole question: it says exactly when the Matrix-Tree Theorem can be applied and classifies the chambers, and gives a compact five-graviton formula outside the decay region. Simplifying the general solution, which is what the source paper left to future work, remains open.", "ai_contribution": "ai_discovered", "attempt_ids": [ "vibemathed:half-collinear-graviton-vertices-as-weighted-root-cone-enumerators:attempt" ], "method_family_ids": [ "vibemathed:half-collinear-graviton-vertices-as-weighted-root-cone-enumerators:method" ], "source_assertion_ids": [ "vibemathed:half-collinear-graviton-vertices-as-weighted-root-cone-enumerators:assertion" ] } ], "attempts": [ { "id": "vibemathed:half-collinear-graviton-vertices-as-weighted-root-cone-enumerators:attempt", "problem_id": "vibemathed:half-collinear-graviton-vertices-as-weighted-root-cone-enumerators", "model": "OpenAI Codex (GPT-5 family)", "provider": "OpenAI", "attempted_at": "2026-08-09T00:00:00.000Z", "human_collaborators": [ "James Peebles", "James Kehoe" ], "exposure": "unknown", "prompt_public": null, "outcome": "From the submission: under human direction, OpenAI Codex proposed the root-cone interpretation, developed the proof, wrote the exact enumeration and verification programs, found the non-decay five-point chamber identity, and drafted the manuscript. A separate model acting as referee reconstructed the published recursion and re-derived the principal claims with fresh code.", "failed_routes": [], "artifacts": [ { "label": "Repository", "url": "https://github.com/jimpeebles/graviton-root-cones", "kind": "code", "license": null }, { "label": "Passing verification workflow", "url": "https://github.com/jimpeebles/graviton-root-cones/actions/runs/31339397929", "kind": "lean-proof", "license": null } ], "sources": [ { "label": "Author repository", "url": "https://github.com/jimpeebles/graviton-root-cones/releases/tag/v0.3.0", "kind": "primary-mathematical-source", "license": null }, { "label": "VibeMathed: Matrix-Tree Obstruction for Half-Collinear Graviton Vertices", "url": "https://vibemathed.com/problem/half-collinear-graviton-vertices-as-weighted-root-cone-enumerators", "kind": "source-assertion", "license": "https://vibemathed.com/data-license" } ], "cost_usd": null, "independence": "unknown" } ], "verifications": [ { "id": "vibemathed:half-collinear-graviton-vertices-as-weighted-root-cone-enumerators:verification", "problem_id": "vibemathed:half-collinear-graviton-vertices-as-weighted-root-cone-enumerators", "solution_event_id": "vibemathed:half-collinear-graviton-vertices-as-weighted-root-cone-enumerators:event", "level": "lean_checked_statement_unaudited", "mathematical_correctness": "supported", "statement_fidelity": "unaudited", "peer_review": "none", "verifier": "VibeMathed (source-reported label)", "verified_at": null, "note": "The conceptual cut, flow and root-cone equivalence is formalized in Lean 4 with no sorry and no custom axioms; principal declarations are guarded by assert_no_sorry with axioms printed, and CI runs lake build --wfail plus leanchecker. Curator check: the linked run completed successfully and the 293-line formalization contains no sorry, admit or native_decide and declares no axioms of its own.\n\nThe label covers the formalized core only. The chamber counts, determinant identities, realizability count and five-point formula are exact-code checked, not Lean-checked. Nobody independent has audited the informal-to-formal correspondence, and no domain expert has endorsed the result. The work is self-published rather than submitted to a venue.", "sources": [ { "label": "VibeMathed: Matrix-Tree Obstruction for Half-Collinear Graviton Vertices", "url": "https://vibemathed.com/problem/half-collinear-graviton-vertices-as-weighted-root-cone-enumerators", "kind": "source-assertion", "license": "https://vibemathed.com/data-license" }, { "label": "Author repository", "url": "https://github.com/jimpeebles/graviton-root-cones/releases/tag/v0.3.0", "kind": "primary-mathematical-source", "license": null } ] } ], "sources": [ { "label": "Author repository", "url": "https://github.com/jimpeebles/graviton-root-cones/releases/tag/v0.3.0", "kind": "primary-mathematical-source", "license": null }, { "label": "VibeMathed: Matrix-Tree Obstruction for Half-Collinear Graviton Vertices", "url": "https://vibemathed.com/problem/half-collinear-graviton-vertices-as-weighted-root-cone-enumerators", "kind": "source-assertion", "license": "https://vibemathed.com/data-license" } ], "recommended_mode": "verify", "recommended_exposure": "result_only", "opportunity_signals": [ { "id": "vibemathed:half-collinear-graviton-vertices-as-weighted-root-cone-enumerators:signal:recent_partial_result", "problem_id": "vibemathed:half-collinear-graviton-vertices-as-weighted-root-cone-enumerators", "kind": "recent_partial_result", "reason": "A source-reported partial result may support bounded expansion.", "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" }