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 \( \mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1) \) structure. For a conserved charge Q, we define an operational copy time \( \tau_{\mathrm{copy}}(Q) \) and show, under explicit locality and hydrodynamic assumptions, that \( \tau_{\mathrm{copy}}(Q) \;\propto\; \bigl(\chi_{micro, Q}^{\mathrm{(2)}}\bigr)^{-1/2} \), where \( \chi_{micro, Q}^{\mathrm{(2)}} \) 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 \( \kappa_{\mathrm{eff}} \). Here \( \kappa_{\mathrm{eff}} \) 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 \( m_{S} = C_\Lambda \sqrt{\kappa_{\mathrm{eff}}\,\chi_{Y}^{(2)}} \), which connects the physical mass \( m_S \) of the singlet scalar to a QICT constant \( C_\Lambda \), the hypercharge susceptibility \( \chi_{Y}^{(2)} \) at \( T_{\star} \), and the FRG parameter \( \kappa_{\mathrm{eff}} \). Using explicit numerical benchmarks \( a = 0.197~\text{GeV}^{-1},\quad D_{Y} \simeq 0.10~\text{GeV}^{-1},\quad \frac{\chi_{Y}^{(2)}}{T_{2}^{\star}} = 0.145 \pm 0.010,\quad \kappa_{\mathrm{eff}} = 0.136 \pm 0.019,\quad C_\Lambda = 1.6 \pm 0.2~\text{GeV}^{-1} \), 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 Z₂ 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.