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on Sidon set autocorrelation constant ($C_{1a}$)

The statement

$C_{1a}$ is 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_{1a} \left(\int_{-1/4}^{1/4} f(x)\ dx\right)^2

for all non-negative $f \colon \mathbb{R} \to \mathbb{R}$ .

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.