This work develops an operator-theoretic framework for analyzing claims of information loss across quantum theory, statistical mechanics, gravitation, and cosmology. The paper introduces observation maps as explicit structural objects and provides a classification scheme distinguishing genuine dynamical non-invertibility from apparent loss arising through coarse-graining, restricted access, or probabilistic conditioning. Canonical examples including decoherence, renormalization group flow, quantum scrambling, black hole evaporation, and cosmological typicality are examined within a unified structural formalism.
Nick Brown (Mon,) studied this question.