Submit progress

on The Ovals Problem (AlphaEvolve problem 19)

The statement

Let $C$ denote the infimal value of $\lambda_0(\gamma)$ , the least eigenvalue of the Schrödinger operator

H_\gamma = -\frac{d^2}{ds^2} + \kappa^2(s)

associated with a simple closed convex curve $\gamma$ parameterized by arclength and normalized to have length $2\pi$ , where $\kappa(s)$ is the curvature. Obtain 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.