Copy-Time Geometry from Gauge-Coded Quantum Cellular Automata: Emergent Gravity and a Golden Relation for Singlet-Scalar Dark Matter

We formulate the Quantum Information Copy Time (QICT) framework for conserved charges under strictly local quantum dynamics and isolate its logically strongest consequence. The theorem-level core is a receiver-optimised variational speed-limit inequality: after projection away from the conserved zero mode, the copy time is bounded from below by the inverse square root of a Liouvillian-squared receiver susceptibility times a local encoding seminorm. This statement is written in a finite-volume operator framework and does not require a diffusive ansatz. We then examine what follows only after additional infrared assumptions. Under a single diffusive slow-mode hypothesis, the variational inequality reduces to the practical scaling relation used in the benchmark computations. That reduction is treated as conditional and is stress-tested numerically rather than promoted by rhetoric. Within the anomaly-free Abelian span relevant for one Standard-Model-like generation, hypercharge selection is elevated to theorem-level status; by contrast, minimal gauge-algebra uniqueness remains explicitly conditional on additional model-selection axioms. The remainder of the manuscript is organised as a documented closure programme built on top of this core. In that closure, a gauge-coded QCA construction, a microscopic benchmark for the transport normalisation, and an electroweak matching convention are combined to produce a resonance-centred Higgs-portal singlet-scalar mass band together with direct-detection, invisible-width, and relic-consistency checks. These latter results are presented as model-dependent consequences of an explicit closure ansatz, not as deductions from locality alone.