What Persists Matters More Than What Changes

Abstract

A reusable world model need not reproduce every future observation exactly. What matters is which distinctions remain stable when forecasts, tasks, or trained instances change. Independently trained models may give different values yet preserve the same relation among matched intervention consequences. This motivates separating state from coordinates and dynamics from realized paths. The same view separates reachability from preference and stable relations from numerical values. Reachability captures possible futures, while persistence tests which relations chosen before evaluation remain stable across selected variations. A smooth deterministic system provides one precise setting, but the underlying perspective is not tied to an explicit model. It also applies to predictive structure embedded in a policy or used in a hybrid system. Persistence itself needs no shared latent coordinates or invariant latent manifold. These distinctions clarify what may change, what should persist, and what evidence supports the claim.