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The sharp constant for the terminal leave of random triangle removal (triangle case of the Joos-Kühn conjecture)

Theorem 1.1: for uniform triangle removal from $K_n$ , $\mathbb E[(F_n/n^{3/2}-1/(2\sqrt2))^2]\to0$ ; hence $F_n/n^{3/2}\to1/(2\sqrt2)$ in probability and $\mathbb E F_n/n^{3/2}\to1/(2\sqrt2)$ . The paper says it does not give the sharp constant for other starting graphs, for general hypergraph removal (the rest of Joos-Kuhn Conjecture 16.2), or a fluctuation law.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 25, 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 sharp constant for the terminal leave of random triangle removal (triangle case of the Joos-Kühn conjecture) · Random triangle removal sharp constant

Confidence: Not scored

Registry verification: lean checked · announcement · partial

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VibeMathed
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Unreleased internal OpenAI model
model · ai model contributor · OpenAI

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Named evidence

VibeMathed record: The sharp constant for the terminal leave of random triangle removal (triangle case of the Joos-Kühn conjecture)

specialist registry · passed

No independent mathematician has checked this yet. Checked here: introduction and Theorem 1.1 read against the triangle case of Joos-Kuhn Conjecture 16.2 as the paper states it. Lean: the challenge lean/ComparatorChallenges/TriangleRemoval.json (solution_module OAI.Combinatorics.TriangleRemoval.Main, present at the pinned commit) is not in the formalization catalogue lean/formalization.yaml. The statement OAI.SharpTerminalLeave.sharp_terminal_leave was read here: it defines the process as a PMF on edge sets run for $\binom n2$ steps from $K_n$ and asserts $L^2$ convergence of $F_n/n^{3/2}$ to $1/(2\sqrt2)$ , convergence in probability and convergence of the normalized mean. That is the headline. Not rebuilt here. Entry is partial because the conjecture covers general strictly balanced hypergraphs.

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Lean formalization (TriangleRemoval main)

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

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The sharp constant for the terminal leave of random triangle removal (triangle case of the Joos-Kühn conjecture)

witness · pending

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

Source ↗

Joos and Kühn, The hypergraph removal process (arXiv 2412.15039), Conjecture 16.2

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

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Artifacts and verifiers

Lean formalization (TriangleRemoval main)

lean artifact · pending

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Compute record

No linked compute attempts recorded.

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This event attributed to Unreleased internal OpenAI model

Joos and Kühn, The hypergraph removal process (arXiv 2412.15039), Conjecture 16.2 evidence for this event

VibeMathed record: The sharp constant for the terminal leave of random triangle removal (triangle case of the Joos-Kühn conjecture) evidence for this event

The sharp constant for the terminal leave of random triangle removal (triangle case of the Joos-Kühn conjecture) evidence for this event

The sharp constant for the terminal leave of random triangle removal (triangle case of the Joos-Kühn conjecture) parent of this event

Lean formalization (TriangleRemoval main) evidence for this event

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