A Universal Infrared Law for Cosmic Acceleration as Irreversible Relaxation (CLEO)

In the era of precision cosmology, the central problem of late-time acceleration is no longer solely the reconstruction of the expansion history, but the identification of structural constraints on the underlying infrared dynamics. Current surveys probe both background and growth sectors with increasing accuracy, raising the question of whether cosmic acceleration reflects a flexible phenomenological description or the manifestation of a constrained effective law. This work addresses this question by formulating cosmic acceleration as an infrared dynamical problem subject to minimal physical constraints and observational selection. In this context, cosmic acceleration is reinterpreted as an effective process of irreversible relaxation in a coarse-grained open system with finite capacity. The presence of occupation-dependent irreversible reset implies loss of microscopic information and effective entropy production, leading to a nonlinear dynamics that cannot be reduced to independent linear dissipative terms. This interpretation establishes a direct connection with open-system physics, stochastic dynamics, and horizon thermodynamics, suggesting that the observed acceleration emerges as a macroscopic manifestation of a relaxation process governed by structural constraints, rather than a fundamental dark-energy term introduced ad hoc. This work establishes the CLEO (Causal Limited Entropic Optimization) framework as a universal infrared law governing the dynamics of bounded open systems with finite activation capacity and occupation-dependent irreversible reset. The notion of universality adopted here is intrinsically coarse-grained and infrared: distinct microphysical systems, when subject to common structural constraints and described at sufficiently large scales, converge to a shared effective dynamical form. Building on previous work, the CLEO equation was introduced as a minimal effective law capable of describing late-time cosmic acceleration under causal and entropic constraints 1. A consistent microphysical realization was subsequently demonstrated through coarse-graining of systems with f inite capacity, correlated activation, and occupation-dependent feedback 2. In the present work, this program is completed by showing that the CLEO structure is not merely a consistent realization, but the universal infrared normal form of a broad class of systems satisfying four minimal conditions: (i) finite state capacity, (ii) bounded activation, (iii) locality at the effective level, and (iv) genuinely collective irreversible reset. It is proven that under these assumptions the effective flow is uniquely constrained, at lowest nontrivial order, to a cubic structure of CLEO type. This establishes CLEO as a universality class of infrared dynamics. A key ingredient of the derivation is the identification of irreducible reset processes. This work shows that any physically meaningful irreversible mechanism associated with finite capacity must be collective, and therefore cannot contribute at linear order in the occupation variable. This enforces a quadratic leading correction which, when combined with bounded activation, yields a cubic closure as the minimal consistent structure. This work further demonstrates that observational constraints provide a selection mechanism within this universal class. In particular, growth-sector data favor a specific realization corresponding to the K2 closure, characterized by a negative nonlinear coupling. This result shows that while the CLEO structure is universal, its microphysical realization is empirically constrained. The domain of validity of the framework is explicitly characterized: the universality applies to coarse-grained infrared dynamics and does not assume a unique ultraviolet completion. Failure modes are identified, including the absence of saturation, dominance of linear processes, and breakdown of locality. Reconstruction invariance is also established, showing that the CLEO structure does not depend on specific parametrizations or inference methods. Taken together, these results elevate CLEO from an effective phenomenological description and a consistent microphysical construction to a universal infrared law governing bounded activation dynamics under entropic constraints. This provides a unified and physically grounded framework for understanding late-time cosmic acceleration and suggests broader applicability to systems with f inite capacity and irreversible dynamics.