A Linear Programming Bound
For any dimension n, let C(n) denote the quantity C(n) := π^n/2/Γ(n/2+ 1) inf_f (r/2)^n f(0)/hat f(0) where f ranges over integrable continuous functions f := ℝ^n → ℝ, not identically zero, with hat f(ξ) ≥ 0 for all ξ and f(x) ≤ 0 for all |x| ≥ r for some r>0.
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-a-linear-programming-bound,
title = {A Linear Programming Bound},
author = {{Cairn Commons contributors}},
howpublished = {\url{https://cairn-commons.com/problems/a-linear-programming-bound}},
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
For any dimension , let denote the quantity where ranges over integrable continuous functions , not identically zero, with for all and for all for some . Establish upper bounds for that are as strong as possible.
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.