Additive-input encoding fails operator-level target-held-out prediction on current Perturb-seq screens

Pooled Perturb-seq screens are often interpreted through a linear steady-state model in which each targeted gene supplies an additive perturbation input. Although this formulation identifies an operator on the observed response subspace in closed form, identifiability alone does not establish that inferred operators generalize to new perturbation targets. We evaluated fixed program-space additive inputs in three Perturb-seq screens -- Replogle K562 essential, Replogle RPE1 essential, and Jost 2020 -- using target-grouped nested cross-validation and matched signal-to-noise linear-truth controls. For inverse operator prediction, real held-out error remained at the predict-zero baseline (0.96, 1.00, and 1.00), whereas matched linear controls achieved 0.18, 0.53, and 0.72. This discrepancy persisted across random K562 target panels, an overdetermined Jost dimension sweep, direction-only fits, ridge and truncated-SVD estimators, and five linear ground-truth ensembles. Forward target-held-out prediction was more nuanced: fixed, footprint, and learned linear encodings modestly beat a predict-training-mean baseline in K562 but not in RPE1 or Jost, and the K562 gains recovered only about 7% of the gap to the matched linear control. On the tested screens, fitted fixed program-space operators should not be interpreted as validated target-generalizing regulatory operators. We release anchor-op, a reproducible toolkit for target-grouped evaluation, identifiability checks, and matched-geometry positive controls for perturbation-response models.