Claims

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2015_02_08_akdemir_ekim: A refereed computer-assisted proof that every graph on 12 vertices has cochromatic number at most 4 and some graph on 13 vertices does not, so z(12) = 4 and z(13) = 5.

2024_09_15_mehta: A computer search confirms z(12) = 4, the one hard value in the table of z(n) for n at most 19; accepted on a Lean proof of z(12) = 4 and of the table built and audited here, not on the curator's credit.

2026_07_26_pitchford: An unrefereed candidate proof released on 2026-07-26 and deposited on Zenodo on 2026-07-28 claims z(20) = 6 from SAT unsatisfiability certificates replayed on one machine; the mathematics is attributed to AI systems.

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