We formalize an observer-dependent extension of the Law of Observation in which the em-pirical feature set is not treated as fixed, but as a time-dependent projection of an underlyingadmissible domain through evolving observer constraints. Rather than assuming that the samedata are merely reinterpreted across eras, we define the accessible feature set Fp(t) as a func-tion of instrumental, cognitive, and linguistic constraint operators. This yields a simple butimportant result: in general,Fp(t1)̸ = Fp(t2),even when the underlying admissible domain remains unchanged. The difference need not implythat reality itself has changed; it can arise because the observer’s distinguishability threshold,segmentation capacity, and descriptive structure have changed. We develop the formal mappingfrom the underlying domain Ω to a time-indexed empirical feature set, define observer-dependentdistinguishability, and introduce projection and persistence operators that make explicit howfeatures emerge, persist, or disappear under changing observational regimes. This provides aclean explanation for shifting empirical domains without requiring forced unification into a singleexplanatory class. The resulting framework predicts non-converged persistent feature spaces,historical changes in accessible empirical structure, and time-dependent mismatches betweendata domains and explanatory frameworks.