Source authenticated

Ryser's conjecture for four-partite hypergraphs with matching number two

Yes, $\tau \le 6$ , closing the case $(r,\nu) = (4,2)$ and putting a proof behind a claim cited from Tuza's unpublished 1979 manuscript for forty-seven years. Ryser's conjecture itself remains open for $r \ge 4$ in general. The general conjecture is claimed disproved for infinitely many large r in OpenAI's October 2026 math release (catalogued as Ryser's conjecture); this (4,2) case is consistent with that claim, which is not yet independently checked.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 13, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. 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: Ryser's conjecture for four-partite hypergraphs with matching number two · Ryser's conjecture, case $(4,2)$

Confidence: Not scored

Registry verification: unreviewed · preprint · partial

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Attribution

VibeMathed
registry · event recorded by

GPT-5.6 Sol
model · ai model contributor · OpenAI

Claude Sonnet 4
model · ai model contributor · Anthropic

Patrick White
human · human collaborator

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Named evidence

VibeMathed record: Ryser's conjecture for four-partite hypergraphs with matching number two

specialist registry · passed

Checked here on 22 September 2026 against arXiv:2609.14281: the abstract states $\tau(H) \le 6$ for four-partite four-uniform $H$ with $\nu(H)=2$ , confirming Tuza's 1979 claim and improving on $\tau \le 7$ , an integrality consequence of Haxell and Scott (2012); the ingredients named are Gyárfás's intersecting-case theorem, a projection lemma and Kőnig's matching theorem. The reference list confirms Tuza's unpublished 1979 manuscript and his 1983 Ars Combinatoria paper. Entered as Partial: one case of Ryser's conjecture, which stays open. The mathematics was not checked here; nine days old, no referee.

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Ryser's conjecture for four-partite hypergraphs with matching number two

preprint · pending

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

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Stronger result in the OpenAI math release

witness · pending

other link supplied by the VibeMathed registry.

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Lineage and corrections

VibeMathed record: Ryser's conjecture for four-partite hypergraphs with matching number two evidence for this event

Ryser's conjecture for four-partite hypergraphs with matching number two parent of this event

This event attributed to Claude Sonnet 4

Ryser's conjecture for four-partite hypergraphs with matching number two evidence for this event

This event attributed to Patrick White

This event attributed to GPT-5.6 Sol

Stronger result in the OpenAI math release evidence for this event

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