Common-Witness Certificates and Sharp Feature Bounds for Counterfactual Image Auditing

Abstract

An image editor may satisfy every regional plausibility constraint separately even when no single latent explanation fits the complete output. We formalize this local-to-global failure using a common witness grade and witness nerve. The framework separates auditing from causal identification: shared exogeneity alone allows every coupling of the regime marginals, whereas an externally justified witness relation yields sharp partial-identification bounds for prespecified image features. Helly-type arguments provide short incompatibility certificates for quasiconvex losses, heterogeneous action strata, and finite witness atlases; a blocker-hypergraph formula gives exact repair counts. Simultaneous confidence regions for the regime marginals give finite-sample outer coverage of the complete identified interval. Controlled MNIST, Morpho-MNIST, and smallNORB studies demonstrate the predicted local-global separation, while synthetic experiments test sharp bounds, certificate recovery, and structured computation. The method audits a declared feature relation and does not identify unrestricted pixel-level counterfactuals.