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

We develop the Quantum Information Copy Time (QICT) framework for conserved charges under strictly local quantum dynamics. The goal is an operational, receiver-optimised notion of how fast charge information can be copied into a distant region, together with a companion susceptibility that quantifies the available linear-response signal in a state-dependent way. Our main technical result is a general variational speed-limit inequality that lower-bounds the copy time in terms of this susceptibility and a local optimisation norm; it holds without assuming diffusion and provides a sharp diagnostic of transport-limited information transfer. We then introduce a controlled diffusive benchmark family (stabiliser-code diffusion models) in which the bound is nearly saturated over several decades, yielding a practical calibration of an effective transport normalisation in the diffusive regime. As a worked, explicitly conditional closure, we describe an electroweak-symmetric matching protocol that combines the calibrated transport scale with hypercharge thermodynamics to infer a characteristic infrared mass scale in the minimal Higgs-portal singlet-scalar dark-matter model, and we provide an uncertainty and prior-sensitivity budget that makes the assumptions transparent.