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.
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 2026-09-28}
} Also: CITATION.cff · Atom feed of results
- Claims
- 0
- Verified
- 0
- Disputed
- 0
- Refuted
- 0
- On the literature board
- 0
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
| Bound | Source | Date |
|---|---|---|
| Goncalves-Oliveira e Silva-Steinerberger | February 2016 | |
| Cohn-Goncalves | December 2017 | |
| Georgiev-Gómez-Serrano-Tao-Wagner [Colab 1] [Colab 2] | 14 May 2025 | |
| Cohn-de Laat-Goncalves (unpublished) | 2025 |
Lower bounds for
| Bound | Source | Date |
|---|---|---|
| Goncalves-Oliveira e Silva-Steinerberger | February 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.