AlphaEvolve problems·alphaevolve:13

A Linear Programming Bound

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

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