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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.arXiv:2009.09316v1 fatcat:33xy5zaefba5jp6nd5bqzeka6q