  We show that the capacity of the Ising perceptron is with high probability
upper bounded by the constant $\alpha_\star \approx 0.833$ conjectured by
Krauth and M\'ezard, under the condition that an explicit two-variable function
$\mathscr{S}_\star(\lambda_1,\lambda_2)$ is maximized at $(1,0)$. The earlier
work of Ding and Sun proves the matching lower bound subject to a similar
numerical condition, and together these results give a conditional proof of the
conjecture of Krauth and M\'ezard.
