Causal Limited Entropic Optimization as the Origin of Late-Time Cosmic Acceleration

The physical origin of late-time cosmic acceleration remains open despite the empirical success of the ΛCDM model at the background level. In particular, the standard description provides an excellent phenomenological fit while leaving unresolved whether acceleration should be interpreted as a true cosmological constant, as an effective infrared phenomenon, or as the macroscopic manifestation of deeper dynamical constraints. This motivates the search for minimal effective laws capable of describing the expansion history while retaining direct physical interpretability. This work introduces the CLEO framework as a new effective law for late-time cosmic acceleration. The proposal is not presented as a complete microphysical theory, but as a minimal dynamical structure designed to capture three physically motivated ingredients: activation, saturation, and cooperative nonlinear response. The resulting law is written as a bounded first-order evolution equation for an effective background variable, u′ = u(3−u)(1+αu), where the prime denotes differentiation with respect to the logarithmic scale factor and α controls the leading departure from pure logistic saturation. The role of this equation is not merely parametric. Its form is selected as the lowest-order effective realization compatible with vanishing dynamics in the inactive regime, finite saturation capacity, and a first-order cooperative correction that preserves a closed infrared description. A central goal of this paper is to show that the CLEO law is not an arbitrary cubic ansatz appended to cosmology after the fact. Rather, it is constructed as a minimal effective dynamical system whose mathematical structure is constrained before comparison with data. To make this statement precise, the paper first defines the effective variable and its relation to the background expansion rate, then derives the law from explicit admissibility requirements, and finally establishes the mapping from the dynamical system to observable quantities such as H(z), luminosity distances, and baryon acoustic oscillation scales. This order is essential: the law must first exist as a coherent dynamical object, and only then be confronted with cosmological measurements. At the observational level, the CLEO framework is tested against standard late-time probes, including cosmic chronometers, Type Ia supernova distances, and baryon acoustic oscillation measurements. The purpose of this comparison is twofold. First, it assesses whether the proposed effective law can reproduce the observed expansion history with a compact parameterization. Second, it clarifies in what sense CLEO behaves similarly to ΛCDM at leading order and in what sense it remains structurally distinct. In this paper, the emphasis is placed on the effective-law level only: no claim is made here of a complete microscopic derivation, universal applicability beyond cosmology, or a full theory of quantum gravity. The main claim advanced in this work is therefore precise and limited. CLEO is proposed as a physically motivated and observationally testable effective law for late-time cosmic acceleration. Its novelty lies in combining minimal nonlinear structure, bounded dynamics, and direct cosmological interpretability within a single framework. If successful, this provides a new way of formulating the acceleration problem: not merely as the inference of a dark-energy component, but as the emergence of a constrained effective law governing the late-time background evolution of the Universe.