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Yes, $\tau \le 6$, closing the case $(r,\nu) = (4,2)$ and putting a proof behind a claim cited from Tuza's unpublished 1979 manuscript for forty-seven years.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.

Yes, $\tau \le 6$, closing the case $(r,\nu) = (4,2)$ and putting a proof behind a claim cited from Tuza's unpublished 1979 manuscript for forty-seven years.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.