The Big Idle: Late-Time Cosmic Acceleration as Informational Saturation within the Stochastic Rupture Framework

Within the Stochastic Rupture (SR) / Strange 4D Rose framework, gravitational curvature emerges from irreversible coarse-grained entropy production associated with horizon-scale decoherence, and operational proper time depends on local informational capacity constrained by the Bekenstein entropy bound. In this paper we extend the framework to cosmology and propose that late-time cosmic acceleration originates from the progressive saturation of informational capacity within a Hubble-scale causal domain. Rather than invoking a fundamental cosmological constant, the acceleration arises dynamically as the coarse-grained entropy-production rate relaxes toward its asymptotic residual value. We give both a phenomenological formulation in terms of an entropy-production rate Γ(t) and a consistent effective realisation as a canonical scalar field φ(x) with a plateau potential. The two descriptions are mutually compatible: the kinetic sector of the scalar field plays the role of the dynamical activity associated with Γ(t). In the asymptotic plateau regime, the slow-roll parameters satisfy εV,ηV → 0, the equation of state approaches w_φ → -1, and the expansion becomes asymptotically de Sitter-like. The observed cosmological constant is interpreted as the asymptotic residual of horizon-scale informational dynamics. We refer to this late-time regime as the Big Idle. The model yields a modest, potentially testable prediction: a small late-time deviation of $w(z)$ from $-1$ as the field relaxes toward its asymptotic idle state. We also indicate how the Big Idle arises from the same mechanism that governs SR branch collapse at the microscopic level, so that cosmological acceleration and the quantum-to-classical transition are unified as two manifestations of informational saturation at different scales.