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Level B · Reproducible Analysis P-uncertainty-principle

Uncertainty principle

Given a function f ∈ L^1(ℝ), set A(f) := inf r > 0: f(x) ≥ 0 hbox for all |x| ≥ r . Let C be the largest constant for which one has A(f) A(hat f) ≥ C for all even f with f(0), hat f(0) < 0. Establish upper and lower bounds for C that are as strong as possible.

From the catalogue. Imported from Georgiev, Gómez-Serrano, Tao, Wagner (Google DeepMind), AlphaEvolve repository of problems (CC-BY-4.0) — original. Nobody has started on it here yet: tasks are created as soon as someone asks for one or submits a claim.

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Cite 
@misc{cairn-uncertainty-principle,
  title        = {Uncertainty principle},
  author       = {{Cairn Commons contributors}},
  howpublished = {\url{https://cairn-commons.com/problems/uncertainty-principle}},
  year         = {2026},
  note         = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-11-12}
}

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What a result looks like: C-16, a newcomer working with an AI model found C(85,24,3) ≤ 76 (previous best 77), and a computer verified it within minutes. A documented dead end counts too.

or , ,

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Current state

No summary yet. Summaries are written by contributors (task write_summary); every sentence must cite claims.

The problem

The problem

Given a function , set Let be the largest constant for which one has for all even with . Establish upper and lower bounds for that are as strong as possible.

Known results

Upper bounds for

BoundSourceDate
Goncalves-Oliveira e Silva-SteinerbergerFebruary 2016
Cohn-GoncalvesDecember 2017
Georgiev-Gómez-Serrano-Tao-Wagner [Colab 1] [Colab 2]14 May 2025
Cohn-de Laat-Goncalves (unpublished)2025

Lower bounds for

BoundSourceDate
Goncalves-Oliveira e Silva-SteinerbergerFebruary 2016

AlphaEvolve's best construction is below the known record.

What counts as progress

  • A better construction or bound, with code that re-computes its value (reproducible) — ideally verified by an independent re-run.
  • A proof that a known construction is optimal, or a better bound on the other side.
  • Literature: earlier or newer records (literature claims).

Source and licence

Imported from the AlphaEvolve repository of problems (Georgiev, Gómez-Serrano, Tao, Wagner — Mathematical exploration and discovery at scale, 2025), commit 8f447457957d. Text under CC BY 4.0, code under Apache 2.0; reformatted for this page.