Claims

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1967_03_01_elliott: Elliott's 1967 theorem asserts that n > 393 points of the plane, not all on one circle or one line, determine at least C(n-1,2) circles; the bound is false, as a circle with n-1 points and one point off it shows.

1994_09_01_balintova_balint: Bálintová and Bálint prove that n points, not all on one circle or one line, determine at least 5n(n-1)/133 circles through exactly three of them, and print the corrected Elliott bound without proof; refereed.

2009_07_03_purdy_smith: Purdy and Smith correct Elliott's 1967 theorem: n points, not all on one circle or line, determine at least 1 + C(n-1,2) - floor((n-1)/2) circles once n > 393, and the bound is attained; only finitely many n remain.

2026_08_20_wrona: A claimed formula for the least number of circles determined by n points that are neither collinear nor concyclic, for every n at least 4, with a Lean development by the claimant; AI-assisted and unreviewed.

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