Adaptive Admissibility as an Operational Consequence of the CLEO–LOP–COUT Framework: From Physical Admissibility to Observable Continuity

The emergence of adaptive behavior across quantum technologies, biological evolution, artificial intelligence, and complex physical systems suggests the existence of organizational principles that extend beyond the specific mechanisms governing each domain. While modern physics successfully describes the fundamental laws constraining physical evolution, and optimization theory explains how adaptive systems improve performance under prescribed conditions, no general framework presently unifies admissibility, long-term persistence, and information transmission into a single operational hierarchy. This work proposes such a framework. Building upon the conceptual architecture of the CLEO–LOP–COUT research program, we introduce the Adaptive Admissibility Principle (AAP) as an operational consequence of a more fundamental hierarchy of physical continuity. Rather than modifying quantum mechanics, thermodynamics, statistical mechanics, or information theory, the proposed framework organizes adaptive dynamics through four successive stages: admissibility, adaptation, persistence, and transmission. The central hypothesis states that adaptive processes never enlarge the physically realizable state space. Instead, adaptation performs constrained exploration within the admissible region established by fundamental physical law. Persistence subsequently ranks admissible trajectories according to their operational stability, while transmission determines whether physically relevant organization survives transitions between successive physical carriers. A mathematical formulation based on nested trajectory spaces is developed. Within this formulation, observable continuity is represented by a continuity functional derived from conditional continuity probabilities rather than introduced as an ad hoc definition. The resulting theory naturally generates a hierarchy of admissible subsets, a dynamical equation for observable continuity, and a set of falsifiable predictions suitable for independent computational and experimental investigation. Entropy-limited quantum reset is presented as the first proposed application of the framework rather than its foundation. Because its admissibility boundary is explicitly determined by Landauer's principle, it provides an ideal benchmark for testing the Adaptive Admissibility Principle under controlled thermodynamic conditions. The framework is presented as a theoretical proposal whose scientific value depends entirely upon future mathematical analysis, numerical simulations, and experimental validation. If confirmed, it would provide a common operational language connecting adaptive control, quantum thermodynamics, reinforcement learning, and the broader problem of physical continuity.