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Vulkin-prog/paper-c-lean

Brice Pouly

Palomar Registrypalomar/PALOMAR-2026-08-26-000012Aug 26, 2026math.NTscore 0

Lean 4 formalization of the first two moments and variance of the number of long constant-stretch starts of an extended Rademacher random completely multiplicative function in a dyadic block, together with the quantitative exponential estimate for the separated homogeneous two-start sum. Uniformly in the critical window, Theorem 1.4 gives the first-moment rate, second falling-factorial-moment convergence, R_2(N,L)=o_C(N^2), and variance convergence; Corollary 11.3 gives the stronger bound R_2(N,L) 0. Both compared statements are conditional on exactly two fully stated ordinary propositions…

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