Claims

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2014_02_25_martinez_roldan_pensado: Martínez and Roldán-Pensado repair Erdős's 1978 argument and prove that n_k exists with n_k = O(k^9), and that n_4 is at most 9 and n_5 at most 37; refereed.

2015_05_19_martinez_sandoval_raggi_roldan_pensado: Martínez-Sandoval, Raggi and Roldán-Pensado derive from a sunflower anti-Ramsey theorem that n_k = O(k^5/log k) when no four points are concyclic; an arXiv manuscript.

2026_09_22_sallerk: A computer-assisted proof that n_4 = 7 under Erdős's general position, using SAT search and ideal saturation in Singular, with lower bounds for n_5, n_6 and n_7; posted on the site's thread with a dated write-up.

2026_09_24_kiichi: A proof that n_4 = 7 under Erdős's general position by a classification of the witness structures of six points, checked end to end in Lean 4; posted on the site's thread with a paper dated 2026-10-03.

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