rk-lean: the directed construction for k-th-power-difference-free sets at every k, with the exponents 0.912145 (k = 4) and 0.950826 (k = 6)
A Lean 4 proof of Krachun's directed (acyclic-block) lower-bound construction for sets of integers with no k-th-power difference, stated and proved for every exponent k >= 2. Let D_k(N) be the largest size of a subset of {1,...,N} no two of whose elements differ by a nonzero perfect k-th power. A pool for k is a nonempty list of blocks (m, sup, H) with pairwise coprime square-free moduli m >= 2, heights H >= 2, and sup a nonempty list of (vertex, rank) pairs with distinct vertices below m, ranks below H, and a strict rank drop along every ordered pair of vertices whose difference is a…
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