The Latent Invariance Principle: An Epistemic Constraint on Measurement Under Indirect Observation

Many phenomena of practical and scientific interest cannot be observed directly. Intent, belief, understanding, disease state, legal scope, risk state, and conceptual mastery are typically accessed through representations such as language, documents, tests, interfaces, symptoms, surveys, or sensor channels. The resulting measurement problem is that correct behavior under one representation does not identify whether a system is tracking the latent phenomenon or responding to surface properties of the representation. The Latent Invariance Principle (LIP) states that, when a phenomenon is observable only through representations, stability of behavior under meaning-preserving representational variation is the admissible empirical evidence that a system is tracking the latent phenomenon rather than the representation. The principle is not a model, algorithm, learning rule, or theory of truth. It is an epistemic and measurement-validity constraint. The analysis formalizes indirect observation using a latent-factor measurement model in which an observable representation arises from a latent phenomenon, a representation channel, and residual variation. Single-representation behavior is shown to be non-identifying: the same observation can be explained by latent tracking or by representation-channel sensitivity. The paper then defines the invariance gap as a diagnostic statistic over valid representations of the same phenomenon and presents an optional orbit/spread formulation for geometric analysis of representational sensitivity. Under LIP, disagreement across valid equivalent representations is evidence rather than noise. The relevant question shifts from whether a system was correct under one form to whether its behavior remained stable when the representation changed and the underlying phenomenon was held fixed.