When Reduction Becomes Lossy: An Intervention-Relative Test of Explanatory Boundaries

Abstract

Can a restricted computational model predict well while omitting distinctions required by its explanatory task? We define boundary sufficiency relative to an outcome, a representation, and a declared family of input interventions. Exact sufficiency requires a common response law on every fiber of the retained representation throughout that family; observational predictive accuracy alone does not establish it. We prove that, under a fixed distribution, the excess optimal log loss from discarding distinctions equals conditional mutual information, and separate this irreducible within-regime loss from the transport loss of a predictor fitted under another regime. Three finite-state synthetic systems implement the test. A strongly lumpable four-state chain is an exact negative control: aggregation incurs zero regret under every tested intervention. A non-lumpable chain has observational regret 0.080 nat per outcome, but regret 0.368 nat after aggregate refitting and 0.733 nat when the observational predictor is frozen under uniform microstate intervention. In an agent–context model with the same observational regret, changing context to oppose the agent gives 1.460 nat frozen-predictor regret. Thirty seeded simulations reproduce these patterns with finite data; sensitivity sweeps include the zero-contrast counterexample. The resulting criterion diagnoses a failure of a specified computational boundary, not an ontological failure of complete microdescription. No empirical claim about neural or cognitive mechanisms follows from these constructed examples.