← The Six-Card Cover Problem
The Six-Card Cover Problem: an Overview
The case r = 6 of the Erdos-Lovasz cover number problem: the chain from fifteen cards to seventeen, and what each stage actually rests on
Mohamed A. Osman · ORCID 0009-0004-5912-999X · independent researcher · 2026-10-19
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Abstract. One pass over the papers. The question, which is the r = 6 case of the problem Erdos and Lovasz posed in 1974, with g(3) = 6, g(4) = 9 and g(5) = 13 known exactly; the two independent routes excluding fifteen cards; the reduction, SAT and certificate layer excluding sixteen; the explicit seventeen-card witness; and, stated plainly, which parts are finite checks, which are certificates, and which remain reading obligations that no certificate can discharge. Priority is not claimed, and the lower bound has not been independently reviewed by a human.
No priority is claimed for any result, and this is not presented as a settled answer. The lower bound is computer-assisted and has not been independently reviewed by a human or by a proof assistant. AI tools were used throughout the work and its review; every computational claim is regenerated by a script or certified by a proof file in code/ and results/ of the repository. Licence: CC BY 4.0 (text), MIT (code).