  We show that with probability exponentially close to $1$, all near-maximizers
of any mean-field mixed $p$-spin glass Hamiltonian on the hypercube $[-1,1]^N$
are near a corner. This confirms a recent conjecture of Gamarnik and Jagannath.
The proof is elementary and generalizes to arbitrary polytopes with
$e^{o(N^2)}$ faces.
