Claims

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1973_05_01_erdos_graham_montgomery_rothschild_spencer_straus: Theorems 13 and 20 of Euclidean Ramsey Theorems I: every finite Ramsey set lies on a sphere, and the orthogonal product of two Ramsey sets is Ramsey, so every rectangular box and its subsets are Ramsey; refereed, JCTA 1973.

1990_01_01_frankl_rodl: Theorem 5.1 of the 1990 paper: every finite affinely independent set is super-Ramsey, with exponentially dense finite witnesses, so every nondegenerate simplex is Ramsey; refereed, J. Amer. Math. Soc. 3 (1990).

1991_07_01_kriz: Theorem 4.3 of the 1991 paper: a finite set with a transitive soluble group of isometries is Ramsey, with a two-orbit extension; so every regular polygon and each regular polyhedron is Ramsey; refereed, PAMS 112 (1991).

1992_10_01_kriz: The 1992 Discrete Mathematics note proves that every trapezoid in its sense, a quadrilateral inscribed in a circle with two parallel sides, is Ramsey; refereed, Discrete Math. 108 (1992).

2026_09_20_palvolgyi: Seven points on a circle, with a transcendental radius, claimed not to be Ramsey; the first claimed disproof of Graham's conjecture that every spherical set is Ramsey, with the proof attributed by the author to ChatGPT.

2026_09_23_openai: A finite set is Ramsey exactly when an explicit linear system over the tensor square of its coordinate field has a solution; kernel-checked in Lean, built and axiom-audited here, with no decision procedure proved.

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