OpenFrontiers
Join
← Back to the index
OP-12108Status unassessedAnalysis

How much can an autocorrelation of a non-negative function resemble an indicator function? (AlphaEvolve problem 3)

How much can an autocorrelation of a non-negative function resemble an indicator function? (AlphaEvolve problem 3). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

MSC 42A85 · Convolution, factorization for one variable harmonic analysis

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 best constant for which one has

∥f∗f∥L2(R)2≤C∥f∗f∥L1(R)∥f∗f∥L∞(R)\|f * f\|_{L^2(\mathbb{R})}^2 \leq C \|f*f\|_{L^1(\mathbb{R})} \|f * f\|_{L^\infty(\mathbb{R})}

for non-negative f ⁣:R→Rf \colon \mathbb{R} \to \mathbb{R}. What is CC?

Lean 4

Not yet attached

No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.

Share a formalization →Verification guide ↗

Background

Repository result category: former record — AlphaEvolve held the record, which has since been improved. See Section 6.2 in "Mathematical Exploration and Discovery at Scale " paper: arXiv:2511.02864. Experiment notebook.

Progress & source assessment

Upper bounds for CC

Bound Source Date
11 Trivial

Lower bounds for CC

Bound Source Date
log⁡16/π=0.88254\log 16/\pi =0.88254 Martin-O'Bryant 1 Apr 2009
0.889220.88922 Matolcsi-Vinuesa 8 Jul 2009
0.89620.8962 Georgiev-Gómez-Serrano-Tao-Wagner [Colab 1] [Colab 2] 14 May 2025
0.9015640.901564 Boyer-Li Nov 2024 / 10 Aug 2025
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). — How much can an autocorrelation of a non-negative function resemble an indicator function? (AlphaEvolve problem 3) linkApache-2.0 (repository license); problem pages reproduced with attribution.

Recorded progress

Add yours →

Nothing recorded yet. A pointer to a paper the entry is missing counts.

Machine attempts

0 recorded

Attempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.

No machine attempts recorded.

Sign in to run an attempt. New accounts start with enough credits for ten.

Discussion

0 notes

Notes are for clarifying the statement, flagging a missing reference, or recording why an approach fails. Claimed solutions belong in a submission, where they can be reviewed.

No notes yet.

Sign in to add a note.