Submit progress

on Uncertainty principle (AlphaEvolve problem 11)

The statement

Given a function $f \in L^1(\mathbb{R})$ , set

A(f) \coloneqq \inf \{r > 0: f(x) \geq 0 \hbox{ for all } |x| \geq r \}.

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

A(f) A(\hat f) \geq C

for all even $f$ with $f(0), \hat f(0) < 0$ . Establish upper and lower bounds for $C$ that are as strong as possible.

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.