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 Z₂ singlet-scalar Higgs-portal dark-matter model. We define an operational quantum information copy time \( \tau_{\mathrm{copy}}(Q)\ \) for a conserved charge Q and introduce a Liouvillian-squared information susceptibility \( \chi^{(2)}_{\mathrm{micro},Q}\ \) based on the Kubo--Mori metric. Under explicit locality, spectral-gap and hydrodynamic assumptions, we formulate a conditional scaling theorem implying \( \tau_{\mathrm{copy}}(Q)\propto \bigl(\chi^{(2)}_{\mathrm{micro},Q}\bigr)^{-1/2}\ \); we provide numerical evidence for this scaling in stabiliser-code diffusion models (Supplemental Material). We then argue that spatially varying copy times naturally define an "optical'' geometry for coarse-grained information propagation: a local information speed \( v_{\mathrm{info}}(x)\propto \tau_{\mathrm{copy}}(x)^{-1}\ \) 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\( \tau_{\mathrm{copy}}\ \). In this perspective, we define the scalar dressing parameter \( \kappa_{\text{eff}} \) 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⋆ in the electroweak-symmetric regime (T⋆≳TEW), and adopting benchmark inputs (with an explicit operational construction of T⋆ given in Supplement~S7), \( \frac{\chi_Y}{T_\star^2} = 0.145 \pm 0.010,\qquad \) \( \kappa_{\mathrm{eff}} = 0.136 \pm 0.019,\qquad \) \( C_\Lambda = 1.6 \pm 0.2 \), we obtain the Golden Relation \( m_S = C_\Lambda \sqrt{\kappa_{\mathrm{eff}}\,\chi_Y} \) and the prediction \( m_S = 58.4 \pm 8.6~\text{GeV},\qquad m_S \in [50,67]~\text{GeV}\ \text{(conservative)} \). We provide a minimal, fully analytic phenomenological consistency check of the Higgs-portal model in the vicinity of the Higgs resonance, using the closed-form expressions for the Higgs invisible width and the spin-independent nucleon cross section. We emphasise that the mass prediction is conditional on the input benchmark intervals and on the diffusive QICT universality class assumptions.