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

We develop a quantitative framework linking quantum information copy time (QICT), gauge-coded quantum cellular automata (QCA), asymptotically safe gravity, and singlet-scalar dark matter. On the microscopic side, we consider an effectively one-dimensional diffusive channel embedded in a gauge-coded QCA with an emergent SU(3)$\times$SU(2)$\times$U(1) structure. For a conserved charge $Q$, we define an operational copy time $\tcopy(Q)$ and show, under explicit locality and hydrodynamic assumptions, that \[ \tcopy(Q)\;\propto\;\bigl(\chisqmicro\bigr)^{-1/2}, \] where $\chisqmicro$ is an information-theoretic susceptibility built from the Kubo--Mori metric and the inverse Liouvillian squared. A conditional theorem establishing this scaling, together with numerical tests on stabiliser-code models up to linear size $L=96$, is formulated below and proved in a Supplemental Material. Within a gauge-coded QCA that realises a single Standard-Model-like generation, we identify hypercharge $Y$ as the unique non-trivial anomaly-free Abelian direction that couples to both quark and lepton sectors, and we exhibit explicitly how, in the $(B,L,Y)$ charge space, anomaly cancellation singles out the hypercharge direction. We further show that, on the anomaly-free subspace, a quadratic susceptibility functional is extremised along the hypercharge direction. We then match the microscopic QICT parameters to a thermal Standard Model plasma at a benchmark temperature $T_\star = 3.1~\text{GeV}$, using ideal-gas expressions for susceptibilities, and adopt an asymptotically safe functional renormalisation group (FRG) benchmark for gravity + SM + neutrinos + a real singlet scalar $S$, summarised in a dimensionless mass parameter $\kappaeff$. Here $\kappaeff$ is treated as a phenomenological parameter, computed in a concrete truncation and then propagated as a prior with quantified uncertainty. Combining these ingredients yields a Golden Relation \[ m_S = \CLambda \sqrt{\kappaeff\,\chisqY}, \] which connects the physical mass $m_S$ of the singlet scalar to a QICT constant $\CLambda$, the hypercharge susceptibility $\chisqY$ at $T_\star$, and the FRG parameter $\kappaeff$. Using explicit numerical benchmarks \[ a = 0.197~\text{GeV}^{-1},\quad D_Y \simeq 0.10~\text{GeV}^{-1},\quad \frac{\chisqY}{T_\star^2} = 0.145 \pm 0.010,\quad \kappaeff = 0.136 \pm 0.019,\quad \CLambda = 1.6 \pm 0.2~\text{GeV}^{-1}, \] we obtain a mass band \[ m_S = 58.1 \pm 1.5~\text{GeV}, \] with a conservative interval \[ m_S \in [56.6,59.6]~\text{GeV}. \] We then perform a minimal but complete phenomenological scan of the $Z_2$ singlet-scalar Higgs-portal model in the $(m_S,\lambda_{HS})$ plane, solving the Boltzmann equation for the relic density and applying current direct-detection and Higgs-invisible constraints. A set of representative viable points lies in the immediate vicinity of the Golden-Relation band near the Higgs resonance.