Problem detail · source-aware
VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
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.
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.
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.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
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. The 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.
Correctness: supported · statement fidelity: unaudited · peer review: none
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.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.