Szemerédi's theorem with random differences
Lean 4 formalization of the main result of the preprint "Szemerédi's theorem with random differences and arithmetic Kakeya" by Gabriel Dahia (arXiv:2610.18859), a threshold for Szemerédi's theorem with random differences. For c = 1/100, k ≥ 3, δ > 0 and p ≥ C n^(-c / log log k), where C is a value of the Ackermann function depending on k and δ, a p-random set D of differences in {1, …, n} has the following property with probability at least 1 - exp(-n^(1 - c / log log k)): every subset of {1, …, n} with at least δn elements contains a k-term arithmetic progression with common difference in…
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