{"id":"palomar/PALOMAR-2026-09-29-000002","url":"https://github.com/ProofFleet/prooffleet/tree/13853222d90d7cff0608c6380d0ee75b0e12473d","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-29-000002-v1.json","repo":"https://github.com/ProofFleet/prooffleet","tags":["math.NT","math.CO","msc:11K38","msc:11N37","msc:11M26","msc:11L15","lean","number-theory","discrepancy","combinatorics"],"score":0,"title":"A Lean formalization of the Erdős discrepancy theorem","trust":"high","domain":"math.NT","source":"palomar","authors":["Sean Huver"],"reviews":0,"subject":"math.NT","summary":"A formalization in Lean 4 and Mathlib of the Erdős discrepancy theorem, proved by Terence Tao in 2015: for every sequence f(1), f(2), … of signs ±1 and every C there are d ≥ 1 and n with |f(d) + f(2d) + ⋯ + f(nd)| > C, so every ±1 sequence has unbounded discrepancy along homogeneous arithmetic progressions. This is the original ±1 formulation, Corollary 1.2 of Tao's paper; its Hilbert-space-valued Theorem 1.1 is not formalized. The proof follows the architecture of Tao's argument: a Fourier-analytic reduction from a sequence of bounded discrepancy to a stochastic completely multiplicative…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-29","reactions":{},"formalized":true,"formalizes":[{"title":"The Erdős discrepancy problem","identifier":"arXiv:1509.05363","relationship":"formalizes"},{"title":"The logarithmically averaged Chowla and Elliott conjectures for two-point correlations","identifier":"arXiv:1509.05422","relationship":"adapts"},{"title":"An averaged form of Chowla's conjecture","identifier":"arXiv:1503.05121","relationship":"adapts"},{"title":"Multiplicative functions in short intervals","identifier":"arXiv:1501.04585","relationship":"adapts"},{"title":"Analytic Number Theory","identifier":"doi:10.1090/coll/053","relationship":"adapts"}]}