Claims

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1981_12_01_simonovits_sos: The 1981 European J. Combin. paper of Simonovits and Sós bounding the extremal family by (pi^2/24 + 1/2 + o(1)) N^2 and refuting the Erdős–Graham guess that the progressions through a fixed element are extremal.

1999_07_01_szabo: Szabó's 1999 European J. Combin. theorem that the extremal family has N^2/2 + O(N^{5/3} (log N)^3) members, with a construction of binom(N,2) + floor((N-1)/4) + 1 sets refuting the Simonovits–Sós conjecture.

2026_07_25_yang: Zhanfu Yang's 2026 preprint reporting t(N) for 3 <= N <= 12 by computation and proving Szabó's lower bound exact for every family with a common element; unrefereed, its computations not rerun by this corpus.

2026_09_09_jenw1n: A Lean proof accepted by the bounty site Conjectures.io in September 2026 that the largest family with pairwise nonempty progression intersections has N^2/2 + O(N) members, Szabó's linear-error question, not the exact value.

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