Claims

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1997_10_01_bollobas_hegyvari_jin: Theorem 3 of Bollobás, Hegyvári and Jin (Discrete Math. 1997): for every increasing sequence of ratios some B with b_{i+1} >= r_i b_i meets A+A+A for every A with gaps in [2,3], so r_3(2,3) does not exist; refereed.

2026_07_06_land: Johan Land's dichotomy: for k >= 3 and 1 <= d_1 < d_2 a ratio for Problem 1112 exists exactly when d_2 >= k + 1; accepted on the Lean port built here, which proves the ratio 192 d_2 (the later bound d_2 + 2 is not built).

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