15.5 When amplification becomes persistent

The learned object is the pair \((\mu _N,c_N)\), where \(c_N\) contains the generator-level progress witnesses and the repair certificate. Suppose an environment morphism sends generators by \(T:H\to H'\) and preserves the convex algebra structures. Naturality of free convex completion gives

Thus the ensemble transports through its generators and weights, provided the feasibility and observer comparisons also transport. This is stronger than copying the final prediction vector: the receiving task obtains a reusable compositional recipe and its warrant.