Source authenticated

The strong thin tree conjecture

Theorem 1.1: there is an absolute $C>0$ such that every finite loopless $k$ -edge-connected multigraph with at least two vertices has a spanning tree $T$ with $|\delta_T(S)|\le(C/k)|\delta_G(S)|$ for all cuts. The proof extracts tree packings on low-resistance edges and iterates a Marcus-Spielman-Srivastava sparsification. The companion gives a deterministic polynomial-time construction, polynomial in the binary input length. Neither paper gives an explicit constant or a new ATSP approximation ratio (constant-factor ATSP was already known by other methods), and spectrally thin trees are not claimed.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The strong thin tree conjecture · Strong thin tree conjecture

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

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Attribution

VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: The strong thin tree conjecture

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Theorem 1.1 of the principal manuscript was read against the conjecture; it gives the strong $C/k$ form for every $k\ge1$ and every finite loopless multigraph on at least two vertices, which also implies Goddyn's original form. No value of $C$ is given. lean/formalization.yaml lists a main result for this manuscript (comparator StrongThinTree, declaration OAI.StrongThinTree.strongThinTree, file OAI/Combinatorics/ThinTrees/Main.lean). ComparatorChallenges/StrongThinTree.lean was read here: it states exactly the headline over finite multigraphs given by endpoint maps with parallel edges distinct. The companion's challenge AlgorithmicThinTrees.json is not in the formalization catalogue; its solution module OAI/Combinatorics/ThinTrees/AlgorithmicMain.lean exists at the pinned commit, and its statement (a stack machine that halts in polynomially many steps in the input length, including binary-encoded multiplicities, and outputs a $C/k$ -thin tree) was read here. Neither was rebuilt here. Permitted axioms: propext, Quot.sound, Classical.choice.

Source ↗

The strong thin tree conjecture

witness · pending

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

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Companion: A polynomial-time construction of strong thin trees

paper · pending

paper link supplied by the VibeMathed registry.

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Lean proof (OAI.StrongThinTree.strongThinTree)

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

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Comparator statement: StrongThinTree.lean

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

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Lean proof of the algorithmic companion (not in formalization catalogue)

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

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Comparator statement: AlgorithmicThinTrees.lean

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

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Goddyn, Some Open Problems I Like, Problem 4 (archived)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

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Artifacts and verifiers

Lean proof (OAI.StrongThinTree.strongThinTree)

lean artifact · pending

Artifact ↗

Comparator statement: StrongThinTree.lean

lean artifact · pending

Artifact ↗

Lean proof of the algorithmic companion (not in formalization catalogue)

lean artifact · pending

Artifact ↗

Comparator statement: AlgorithmicThinTrees.lean

lean artifact · pending

Artifact ↗

Compute record

No linked compute attempts recorded.

Lineage and corrections

Lean proof (OAI.StrongThinTree.strongThinTree) evidence for this event

The strong thin tree conjecture parent of this event

This event attributed to Unreleased internal OpenAI model

Comparator statement: AlgorithmicThinTrees.lean evidence for this event

Lean proof of the algorithmic companion (not in formalization catalogue) evidence for this event

Goddyn, Some Open Problems I Like, Problem 4 (archived) evidence for this event

Companion: A polynomial-time construction of strong thin trees evidence for this event

VibeMathed record: The strong thin tree conjecture evidence for this event

The strong thin tree conjecture evidence for this event

Comparator statement: StrongThinTree.lean evidence for this event

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