Quantum Information Copy Time and Gravity from Relative-Entropy Sources: Global Manuscript with Microscopic Control and Reproducible Artefacts

We present a consolidated, referee-auditable formulation of the Quantum Information Copy Time(QICT) program. A single localized information-theoretic object—relative entropy, equivalently amodular-energy deficit—is shown to (i) control restricted operational distinguishability via dataprocessing and Pinsker-type inequalities and (ii) coincide with the variational functional enteringentanglement-equilibrium gravitational closure through the exact modular identity D = ∆⟨K⟩−∆S. We separate exact information-theoretic statements from regime-dependent field-theoreticassumptions (local modular Hamiltonians in small causal diamonds) and from microscopic proposals.A reproducible microscopic lattice toy model numerically verifies the operational bounds and themodular identity with embedded figures generated by code. Finally, we include a concrete discreteinformation-field model class formulated by a local gauge-invariant action on a causal cell complexand specify nonperturbative decision criteria under which General Relativity may arise as an infrareduniversality class, without claiming that this emergence is established here.