QICT Cosmology with Complex-Phase Dark Sector: Late-Time Dynamics and Implications for H₀ and S₈ Tensions

We present a full operational formulation of Quantum Information Copy Time cosmology in which the infrared scale entering the dark sector is defined by the largest distance over which a fundamental information unit can be copied within one Hubble time. Evaluating the Cohen–Kaplan–Nelson collapse bound at that copy horizon yields a falsifiable effective dark sector with 0 < c_Q ≤ 1. The homogeneous source is formulated through a Hermitian reduced-state quadrature, placing the dependence on ℜ[α] squarely within standard open-system quantum mechanics. In a local monitored Markovian universality class we recover diffusive copy transport and the familiar late-time branch with leading source ρ_Q ∝ H, and we identify the precise open-system structure that promotes this baseline branch into a quantum-limited saturation regime. Rather than introducing a pole-like regulator or an additive constant latency, we promote the late-time response ratio Ξ = c_Q²/D_∞ to a two-component response consisting of an asymptotic saturation floor and a switched transport contribution. This yields a background source of the form ρ_Q = ρ_sat + νHS (z;z_t,∆z), where the activation function is motivated by the same logistic open-system kinetics that controls the copy-sector transition. We further derive the four effective background parameters analytically within the QICT effective theory: the transport amplitude follows from the copy horizon plus the CKN bound, the transition redshift from quantum-speed-limit onset, the transition width from logistic open-system relaxation, and the matter fraction from flatness plus late-time equality. We further derive a Green–Kubo interpretation of the asymptotic transport plateau and present an explicit de Sitter/KMS locking scenario for D_⋆. The manuscript includes validated late-time geometric diagnostics, Pantheon+SH0ES covariance-ready supernova handling, effective perturbative stability conditions, semi-analytic growth and matter-power forecasts, and a concrete precision-cosmology implementation path through CLASS/CAMB and CMB/lensing/LSS likelihoods.