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

arXiv:2609.03973v1 Announce Type: new 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.