Residual Consistency Cannot Certify Pathology: Task-Observable Falsification for Generative Sparse-View CT

Generative sparse-view CT can improve global image quality while suppressing task-relevant evidence. We present task-observable falsification, an audit that selects relatively lower-observability tasks within a declared family before reconstruction, then evaluates their transfer with paired pathology counterfactuals and factorial physics dosing. A null-space proposition establishes that a score computed only from measurements and their reconstruction cannot universally certify a null-space-sensitive task. For a conditional VAE followed by five SART updates, a validation-locked residual rule appears successful on 32 test images, but that cohort contains no failures. A post-lock scale challenge falsifies this pipeline-specific rule: paired lesion scales change residual by at most $7.6\times10^{-9}$, failure AUROC is 0.504, and all 108 accepted smaller-signal cases fail. Without reconstruction outcomes, a constrained search reduces RMS measurement SNR by 6.2\% relative to an isotropic control. The resulting factorial audit separates initialization from refinement: five SART updates lower FBP-seeded contrast recovery from 0.939 to 0.797 but raise VAE, diffusion, and U-Net recovery from 0.103/0.766/0.813 to 0.844/0.822/0.907. The frozen protocol reproduces on 51 slices from 27 patients excluded from search, where failure counts are 0/51 for FBP, 51/51 for SART, VAE, and diffusion, and 18/51 for U-Net. Task observability therefore defines an acquisition-level audit envelope, not an individual-case certificate.