The Projection–Admissibility Principle: Structural Constraints on Effective Physical Description

Physical theories operate as effective descriptions, tracking only those distinctions that remain stable and predictive under finite control. Across quantum theory, statistical physics, gravity, and information theory, recurring qualitative features—probability, irreversibility, universality, entropy production, and breakdown of description—appear largely independent of microscopic detail. This paper isolates a minimal structural core underlying these phenomena. We formalize effective description as arising from an invertible underlying evolution composed with a noninjective projection defined only on an admissible domain. We then prove a projection–admissibility obstruction theorem: once admissibility fails along a trajectory, the induced effective evolution admits no global measurable right inverse. Irreversibility and probabilistic weighting follow as structural consequences of this noninvertibility rather than as additional postulates. The results are classification statements about any stable effective description and introduce no new microscopic dynamics. Modal Triplet Theory is discussed as a concrete realization demonstrating that the abstract conditions of the principle can be satisfied explicitly. The Projection–Admissibility Principle thus provides a unifying structural explanation for the form and limits of effective physical laws.