Exact finite-instance bounds for Chowla's cosine problem: theorem-grade dip brackets, a repaired sum-of-squares verifier, the elementary fractional optimum, and bounded verification of the small-n theory
Chowla's cosine problem asks whether $\lambda(n)=\inf_{|A|=n}(-\min_x\sum_{a\in A}\cos ax)$ can satisfy $\lambda(n)\le c\sqrt n$ for arbitrarily small $c$. This