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

We develop an information-theoretic route from microscopic conserved-charge dynamics to an infrared mass prediction in the minimal \mathbb{Z}_2 singlet-scalar Higgs-portal dark-matter model. We define an operational quantum information copy time \tau_{\rm copy}(Q) for a conserved charge Q, and introduce a Liouvillian-squared information susceptibility \chi^{(2)}_{{\rm micro},Q} based on the Kubo–Mori metric. Under explicit locality, spectral-gap, and hydrodynamic assumptions, we formulate a conditional scaling theorem implying \tau_{\rm copy}(Q)\;\propto\;\big(\chi^{(2)}_{{\rm micro},Q}\big)^{-1/2}. We provide numerical evidence for this scaling in stabiliser-code diffusion models (Supplementary Material). We then argue that spatially varying copy times naturally define an “optical” geometry for coarse-grained information propagation: a local information speed v_{\rm info}(x)\propto \tau_{\rm copy}(x)^{-1} induces an effective metric, and diffeomorphism invariance in the long-wavelength description implies that the Einstein–Hilbert term is the leading infrared operator, with higher-derivative corrections controlled by gradients of \tau_{\rm copy}. In this perspective, we define the scalar dressing parameter \kappa_{\rm eff} intrinsically from microscopic QICT susceptibilities in the electroweak-symmetric regime; asymptotic-safety FRG results, when invoked, serve only as an external cross-check rather than as a foundational assumption. Within a gauge-coded QCA realising a Standard-Model-like generation, anomaly cancellation singles out hypercharge Y as the unique non-trivial anomaly-free Abelian factor coupling to both quarks and leptons. Matching to a thermal Standard Model plasma at a reference temperature T_\star in the electroweak-symmetric regime (T_\star \gtrsim T_{\rm EW}), and adopting benchmark inputs (with an explicit operational construction of T_\star given in Supplement S7), \frac{\chi_Y}{T_\star^2}=0.145\pm 0.010,\qquad \kappa_{\rm eff}=0.136\pm 0.019,\qquad C_\Lambda=1.6\pm 0.2, we obtain the Golden Relation m_S \;=\; C_\Lambda\,\sqrt{\kappa_{\rm eff}\,\chi_Y}, and the prediction m_S = 58.4 \pm 8.6~{\rm GeV},\qquad m_S\in[50,67]~{\rm GeV}\ \ (\text{conservative}). We provide a minimal, fully analytic phenomenological consistency check of the Higgs-portal model in the vicinity of the Higgs resonance, using closed-form expressions for the Higgs invisible width and the spin-independent nucleon cross section. We emphasize that the mass prediction is conditional on the input benchmark intervals and on the diffusive QICT universality-class assumptions.