Quantum Information Copy Time (QICT) Cosmology with an Open-System Complex-Phase Dark Sector: Rigorous Foundations and Global Background-Level Feasibility Tests Toward H0 and S8 Alleviation

We formulate a late-time effective cosmological framework in which the infrared scale associated with a dark-energy sector is defined operationally through a quantum information copy time. The proposal is local rather than teleological: the relevant infrared length is the largest scale \( L_{\rm copy}(t) \) over which a minimal unit of coarse-grained quantum information can be copied within one Hubble time. Combined with the Cohen–Kaplan–Nelson collapse bound, this prescription yields a falsifiable contribution of the form \( \rho_Q\propto L_{\rm copy}^{-2} \) together with the hard requirement \( 0 < c_Q\le 1 \). We also write an explicit open-system realization in which the real homogeneous source is the expectation value of a Hermitian quadrature, so that the dependence on 2Re[α] is compatible with standard quantum mechanics. A companion note included in the submission package places the late-time diffusion closure inside a broader variational copy-time framework, so the cosmological reduction is not introduced as a stand alone fitting device. Relative to earlier drafts, the present version sharpens the logic in four ways. First, the principal closures are stated as conditional theorems under a minimal hypothesis set. Second, the diffusion-class background branch is explicitly interpreted as one late-time reduction within a broader copy-time theory. Third, several relative-uniqueness and no-go statements are made explicit, so that the framework is not presented as an arbitrary phenomenological ansatz. Fourth, the evidential scope is kept deliberately modest: the paper remains an effective-theory construction with background-level feasibility diagnostics, not a claim of unique ultraviolet completion, perturbation-complete Boltzmann implementation, or full Planck-likelihood validation.