Claims

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1947_12_01_hall: Hall's 1947 remark that the Sidon set -8, -6, 0, 1, 4 (equivalently 1, 3, 9, 10, 13) lies in no perfect difference set modulo any v, refuting the conjecture for every modulus; recognized as the first disproof in 2025.

2025_10_22_alexeev_mixon: The Sidon set 1, 2, 4, 8 extends to no perfect difference set modulo p^2+p+1 with p prime, and 1, 2, 4, 8, 13 to none modulo any v, disproving the prize conjecture; the authors verified both in Lean.

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