Matrix-Tree Obstruction for Half-Collinear Graviton Vertices
Everything below was recorded by a tool. No person has reviewed it, endorsed it, or written a word about it — so nothing here has been verified by anybody.
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.
Context
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.
A specific technical obstruction stated in one March 2026 paper, in an active corner of amplitudes research with prominent authors, but only months old and narrow in reach.
People
Projects
Nobody is running a project on this. A project is a stated goal, a thread, and one thing somebody else could do. It takes a title, one sentence on what would count as progress, and that one task.
Interest
Nobody has said they are looking at this. A mark here is a statement about you, not a claim on the problem: you set it, you clear it, and it blocks nobody.
Attempts
No person has examined this. There is 1 attempt here and 1 machine check recorded against it. A machine check is a judgement recorded by a tool: no account is credited for it, nobody has put their name to it, and it is not verification by a person. Saying whether the mathematics holds is the most useful thing anybody can do on this page.
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.
Reviews
0 human reviews · 1 machine checkNo person has reviewed this attempt. 1 machine check below — a machine check is not human verification.
Machine check · not human verification
machine: partially checkedscope Lean formalization of the core argument; statement correspondence not independently audited
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.
No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.
Endorsements
0 endorsementsNo one has endorsed this attempt. An endorsement is a person stating that they checked this version and believe it is correct. None has been recorded — which is information, not an omission.
Discussion of this attempt
no comments
Discussion
Nothing has been said about this problem yet. Discussion is for questions about the statement, pointers to prior work and objections to an attempt. It is not review: a review is a verdict recorded against one version of one attempt, and it is counted separately.
Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.