arXiv:2610.29275v1 Announce Type: cross Abstract: Let $C$ be an $[n,k,d]_q$ Griesmer code, where $q=p^f$ with $p$ prime, and write $e=\nu_p(d)$. Ward conjectured that $C$ is $p^{\max\{0,e-f+1\}}$-divisible. In this paper, we prove this conjecture.