PAD: JOINT INTERPRETATION OF PERTURBATION EVIDENCE

Inferring causal direction from single- and double-perturbation assays requires understanding how a response depends on its background. The question is how much predictive value independent scoring must lose, and which measured sources change a decision. The central insight is that exchange-invariant evidence can carry no directional sign on its own yet determine how another channel should be read. PaD implements this conditional interpretation with channel-specific and joint kernel terms. Under balanced exchange symmetry with invariant context, arbitrary nonlinear additive scoring recovers at most half of the classification gain available through joint access; exchange-consistent additive decisions recover none. A common-threshold condition makes the half-gain bound exact. Observation-level bounds and independent-test certification connect this limit to fitted learners: nine simulated classifiers attain risk upper bounds at most 9.534%, below the sharp additive limit of 16.361%. Measured yeast comparisons attribute the empirical benefit to joint access rather than to a specific kernel mixture. On the Jonikas development panel, exchange-invariant measurement metadata can change directional decisions, with contributions that depend on the other retained inputs. Source removal, refitted block-mismatch controls and resampling of the evaluation records assess these contributions and their sensitivity to record composition. Together, the results connect a sharp limit on independent scoring to the practical evaluation of which evidence changes which decision, and under which retained context.