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on Erdős minimum overlap constant ($C_{1b}$)

The statement

$C_{1b}$ is the largest constant for which one has

\sup_{x \in [-2,2]} \int_{-1}^1 f(t) g(x+t)\ dt\geq C_{1b}

for all non-negative $f,g: [-1,1] \to [0,1]$ with $f+g=1$ on $[-1,1]$ and $\int_{\mathbb{R}} f = 1$ , where we extend $f,g$ by zero outside of $[-1,1]$ .

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.