Panoptic Quality (Kirillov et al., 2019) scores an instance segmentation as the sum of the matched intersection-over-union values over $|TP| + \tfrac12|FP| + \tfrac12|FN|$. This submission treats the metric as a function of those four counts and proves the exact identities that govern how it moves when one prediction is added, removed, or duplicated.

The inclusion rule: a candidate that matches with probability $p$ and IoU $j$ raises the expected score if and only if $p\,j > \mathrm{PQ}/2$, because the denominator rises by exactly $\tfrac12$ whether the candidate matches or not. The removal rule is its mirror image, and the two are inverse. Under evaluators that accumulate every pair above the threshold instead of a one-to-one matching, a duplicate of a matched prediction with IoU $v$ raises the score if and only if $v > \mathrm{PQ}$, and no reweighting of false positives and false negatives removes this incentive; under one-to-one matching the same duplicate is a false positive and lowers the score exactly when false positives carry positive weight.

Two further statements concern the matching itself and the data. With the strict threshold $\mathrm{IoU} > \tfrac12$ a prediction matches at most one of any family of disjoint annotations, and the threshold is sharp: at $\tfrac12$ a prediction can tie with two. When two annotators of the same image disagree in their instance counts, the Panoptic Quality of any prediction scored against both is strictly below $1$, by a margin of half the disagreement.

All statements are elementary and their proofs are short; their value is that a competition, a benchmark, or a paper can cite the exact condition rather than an intuition. They were used to select the operating point of a solar-filament segmentation pipeline and to diagnose a metric-inflating evaluator.