Open Research Index

MI-32: Lean formalization of the parity and positive-polynomial upper bound

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Palomar Registrypalomar/PALOMAR-2026-09-14-000006Sep 14, 2026math.PRscore 0

A Lean 4 formalization of the MI-32 upper bound, that is, of the Latała-Świątkowski conjecture that for every regularity parameter alpha >= 1 there is a constant C > 0, independent of the dimension and of the entry laws, with E||X|| = 1. Here ||.|| is the Euclidean operator norm, M(X) is the sum of the largest row and column standard deviations, and D(X) is the max-min weak moment at order log(k+1) taken over one shared deterministic deletion set on both axes. The probability space is arbitrary and the subunit order log 2 at k = 1 is kept literally. The selected theorem MI32.main_upper…

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