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on An autocorrelation problem related to Sidon sets (AlphaEvolve problem 2)

The statement

Let $C$ denote the largest constant for which one has

\max_{-1/2 \leq t \leq 1/2} \int_\mathbb{R} f(t-x) f(x) dx \geq C \left(\int_{-1/4}^{1/4} f(x) dx\right)^2

for all non-negative $f \colon \mathbb{R} \to \mathbb{R}$ . What is $C$ ?

What gets accepted

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