AlphaEvolve problems·alphaevolve:13
A Linear Programming Bound
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For any dimension $n$, let $C(n)$ denote the quantity $$ C(n) \\coloneqq \\frac{\\pi^{n/2}}{\\Gamma(n/2+ 1)} \\inf_{f} \\frac{(r/2)^n f(0)}{\\hat f(0)}$$ where $f$ ranges over integrable continuous functions $f \\coloneqq \\mathbb{R}^n \\to \\mathbb{R}$, not identically zero, with $\\hat f(\\xi) \\geq 0$ for all $\\xi$ and $f(x) \\leq 0$ for all $|x| \\geq r$ for some $r>0$. Establish upper bounds for $C(n)$ that are as strong as possible.
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qed.bot, “A Linear Programming Bound”, https://qed.bot/t/alphaevolve-13, as of 30 Sep 2026.