Interpolation Is Not Invariance: Pair Count Is Not Coverage in Transformation Audits

Counting equivalent pairs is the usual way to report how thoroughly a transformation audit covers a model, and it overstates what the audit constrains. Pairs drawn from one semantic object are correlated, and on a complete orbit graph most of them are algebraically redundant. We therefore separate four quantities that a raw count conflates: edge count $m$, effective contrast rank $s$, population support rank $r$, and graph spectral gap $\eta$. In a rank-$r$ Gaussian contrast model, a calibrated reader that is invariant on the population exists exactly when the anchor has a component in $\ker T$. Failing that, an audit of rank $s