Observer-Dependent Feature Emergence: Time-Dependent Observational Projections in the Law of Observation

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 underlying
admissible domain through evolving observer constraints. Rather than assuming that the same
data 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 but
important result: in general,
Fp(t1)̸ = Fp(t2),
even when the underlying admissible domain remains unchanged. The difference need not imply
that reality itself has changed; it can arise because the observer’s distinguishability threshold,
segmentation capacity, and descriptive structure have changed. We develop the formal mapping
from the underlying domain Ω to a time-indexed empirical feature set, define observer-dependent
distinguishability, and introduce projection and persistence operators that make explicit how
features emerge, persist, or disappear under changing observational regimes. This provides a
clean explanation for shifting empirical domains without requiring forced unification into a single
explanatory class. The resulting framework predicts non-converged persistent feature spaces,
historical changes in accessible empirical structure, and time-dependent mismatches between
data domains and explanatory frameworks.