Uncertainty principle (AlphaEvolve problem 11)
Uncertainty principle (AlphaEvolve problem 11). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.
Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.
Problem statement
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.
Lean 4
No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.
Background
Repository result category: worse than record — AlphaEvolve did not reach the best known result. See Section 6.6 in "Mathematical Exploration and Discovery at Scale " paper: arXiv:2511.02864. Experiment notebook.
Progress & source assessment
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| Cohn-de Laat-Goncalves (unpublished) | 2025 |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 |
- [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). — Uncertainty principle (AlphaEvolve problem 11) 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 recordedAttempts 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.
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Discussion
0 notesNotes 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.
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