= Zero-variance boundary of an overflow constraint
{title2=$\mathbb P(X\geq C)=\mathbf1_{\{m\geq C\}}$}
If a random variable has <variance> zero and mean $m$, it equals $m$ almost surely. For a target probability strictly between zero and one, $\mathbb P(X\geq C)$ meets the target exactly when $m<C$. Substituting zero variance into a positive-variance non-strict quantile constraint incorrectly includes $m=C$, where the overflow probability is one. The distinction comes from the atom at the threshold.
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