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

arXiv · AI, language, vision and robotics · article · Sep 14, 2026 · UTC

Counting equivalent pairs is a common way to report transformation-audit coverage, but it can substantially overstate the constraints imposed by an audit: pairs generated from the same semantic object are correlated, and complete orbit graphs contain algebraically redundant edges. We therefore distinguish four complementary quantities---edge count $m$, effective contrast rank $s$, population support rank $r$, and graph spectral gap $η$---and characterize their roles in audit coverage and deployment reliability. Under a rank-$r$ Gaussian contrast model, a population-invariant calibrated reader

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