Matrix-Tree Obstruction for Half-Collinear Graviton Vertices

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.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Aug 9, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Matrix-Tree Obstruction for Half-Collinear Graviton Vertices · Graviton root cones

Confidence: Not scored

Registry verification: lean checked · announcement · partial

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Attribution

VibeMathed
registry · event recorded by

James Peebles
human · human collaborator

James Kehoe
human · human collaborator

OpenAI Codex (GPT-5 family)
model · ai model contributor · OpenAI

Evidence vector

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Named evidence

VibeMathed record: Matrix-Tree Obstruction for Half-Collinear Graviton Vertices

specialist registry · passed

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.

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Matrix-Tree Obstruction for Half-Collinear Graviton Vertices

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Repository

code · pending

code link supplied by the VibeMathed registry.

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Passing verification workflow

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.