  The asymptotic study of class numbers of binary quadratic forms is a
foundational problem in arithmetic statistics. Here, we investigate finer
statistics of class numbers by studying their self-correlations under additive
shifts. Specifically, we produce uniform asymptotics for the shifted
convolution sum $\sum_{n < X} H(n) H(n+\ell)$ for fixed $\ell \in \mathbb{Z}$,
in which $H(n)$ denotes the Hurwitz class number.
