On Graham's rearrangement conjecture (Pham–Sauermann)
A Lean 4 / Mathlib formalization of H. T. Pham and L. Sauermann, "On Graham's rearrangement conjecture" (arXiv:2602.15797v1). Graham conjectured in 1971 that for every prime p, every subset S of Z_p \ {0} has an ordering whose partial sums are pairwise distinct. The formalization proves the paper's main theorem (Theorem 1.2): for every 0 0 such that, for every prime p, every S ⊆ Z_p \ {0} with C_α ≤ |S| ≤ p^(1-α) has such an ordering. It also proves the paper's anticoncentration bounds for the sum of a uniformly random m-element subset R of a set S ⊆ Z_p with |S| ≥ 2: the probability that…
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