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 develop a falsifiable effective framework in which the infrared scale enteringholographic dark energy is defined operationally by a quantum-information copying time. For aphysical separation L at cosmic time t, the copy time τcopy (L, t) is the time required to replicatea minimal unit of quantum information across that separation. The copy horizon Lcopy(t) is fixed locally by τcopy(Lcopy, t) = ξ/H(t), with ξ = O(1). Combining this operational infraredscale with the Cohen–Kaplan–Nelson gravitational-collapse bound motivates an energy density ρQ(t) = 3κM2PlcQ(t)/L2copy(t) and promotes “saturation” to a one-sided falsifiable inequality 0 < cQ ≤ 1 (Hard Consistency Bound). We relate τcopy to coarse-grained entropy productionand adopt a late-time diffusion-limited closure τcopy ≈ L2/D∞(t), which closes the backgrounddynamics and yields an analytic expansion history E(z) = H(z)/H0. We describe a late-timelikelihood based on binned Pantheon+ supernovae and SDSS DR16 BAO consensus distances,with the sound horizon treated as a nuisance parameter when desired.