Observational Closure Degeneracy in Effective Infrared Dynamics: Demonstrated Results, Conditional Models, and Open Derivations in the CLEO–LOP–COUT

The CLEO–LOP–COUT programme proposes a hierarchical framework for effective physical organization based on three successive layers: bounded causal–entropic activation (CLEO), persistence under irreversible loss (LOP), and transmission of organization across successive physical carriers (COUT). Previous work established a restricted class of effective dynamics characterized by finite capacity, saturation, cooperative response, and mesoscopic realizability, and explored its implications for infrared cosmology, observational phenomenology, adaptive dynamics, persistence, and information transmission. Nevertheless, the connection between the internal effective dynamics and cosmological observables has remained dependent on phenomenological closure assumptions rather than on an independently derived physical operator. The present work introduces a rigorous epistemic reformulation of the programme through an explicit separation between demonstrated results, modeled relations, and open derivations. A revised ontology distinguishes the internal mesoscopic activation variable, the observable cosmological infrared flow, and the closure operator relating them. Within this formulation, the exact identity between the logarithmic evolution of apparent-horizon entropy and the cosmological infrared flow variable is established for spatially flat FLRW spacetimes under the standard assumptions of horizon thermodynamics. Consequently, the central unresolvedcosmological problem is reduced to the derivation of the physical operator connecting the internal causal–entropic state to the observable logarithmic horizon-entropy flow. Two general mathematical results constitute the methodological core of the paper. First, it is demonstrated that any continuous strictly monotonic internal trajectory combined with an unrestricted monotonic observational closure is locally observationally equivalent to an arbitrary continuous monotonic target history. Second, it is proven that every finite-order local differential closure associated with a one-dimensional autonomous internal flow reduces, along its own solutions, to an effective algebraic closure and therefore inherits the same observational degeneracy. These results identify unrestricted closure freedom—not the internal dynamics itself—as the principal source of observational non-identifiability. A uniform epistemic framework is then introduced, distinguishing demonstrated (D), modeled (M), open (O), and conditionally demonstrated (D|M) results through an explicit weakest-link rule governing evidential propagation. This classification is applied retrospectively to the accumulated CLEO–LOP–COUT programme, preserving its conceptual architecture