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OP-12110Status unassessedCombinatorics

Erdős minimum overlap problem (AlphaEvolve problem 5)

Erdős minimum overlap problem (AlphaEvolve problem 5). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

MSC 11B75 · Other combinatorial number theory

Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.

Licensed source statementAs of Repository at commit 8f44745 (2026-07-11); the repository records AlphaEvolve results, not current research statusSource & evidence ↓
Read original source ↗ 0Submit progressLean 4 ↓Discussion (0)

Problem statement

Let CC be the largest constant for which

sup⁡x∈[−2,2]∫−11f(t)g(x+t)dt≥C\sup_{x \in [-2,2]} \int_{-1}^1 f(t) g(x+t) dt\geq C

for all non-negative f,g:[−1,1]→[0,1]f,g: [-1,1] \to [0,1] with f+g=1f+g=1 on [−1,1][-1,1] and ∫Rf=1\int_\mathbb{R} f = 1, where we extend f,gf,g by zero outside of [−1,1][-1,1]. What is CC?

Lean 4

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Background

Repository result category: world record — AlphaEvolve improved on the best known result recorded at the time. See Section 6.2 in "Mathematical Exploration and Discovery at Scale " paper: arXiv:2511.02864.

Progress & source assessment

Upper bounds for CC

Bound Source Date
0.3809270.380927 Haugland 2016
0.3809240.380924 Georgiev-Gómez-Serrano-Tao-Wagner [Colab 1] [Colab 2] 14 May 2025
0.3808760.380876 Yuksekgonul et al. Jan 2026

Lower bounds for CC

Bound Source Date
11 Trivial
0.3790050.379005 White 2022
References
  1. [1]Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Repository of problems accompanying “Mathematical exploration and discovery at scale” (arXiv:2511.02864), github.com/google-deepmind/alphaevolve_repository_of_problems (commit 8f44745, 11 July 2026). — Erdős minimum overlap problem (AlphaEvolve problem 5) linkApache-2.0 (repository license); problem pages reproduced with attribution.

Recorded progress

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Machine attempts

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Discussion

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