Submitted:
24 February 2026
Posted:
06 March 2026
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Abstract
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 \( \chi^{(2)} \) based on the Kubo--Mori metric. Empirically, across several decades in \( \chi^{(2)} \) we find the robust scaling \( \tau_{\mathrm{copy}}(Q)\propto (\chi^{(2)}_{Q})^{-1/2}\ \) (Table 1 and Figure 1). Analytically, a general linear-response/Cauchy-Schwarz inequality bounds the growth rate of any receiver-optimised overlap by \( \sqrt{\chi^{(2)}_Q}\ \); for a fixed operational threshold \( \eta\ \) and normalised sender/receiver operators this implies the conditional lower bound \( \tau_{\mathrm{copy}}\gtrsim \eta/\sqrt{\chi^{(2)}_Q}\ \) under mild regularity/monotonicity assumptions (Closure Supplement, Section "Copy-time bound''). We also provide stabiliser-code diffusion benchmarks that illustrate the scaling and help calibrate normalisations in the diffusive universality class. 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 Yas the unique non-trivial anomaly-free Abelian factor coupling to both quarks and leptons; we also provide a self-contained anomaly calculation (see the Closure Supplement, "Hypercharge from anomaly constraints'') and emphasise that this selects a one-dimensional anomaly-free direction; it does not exclude embeddings or additional hidden sectors. This is a minimal-factor selection under stated assumptions and does not exclude embeddings, additional hidden sectors, or discrete quotients. 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 the Closure Supplement (Point~(6)) and an explicit interacting thermal-QCA susceptibility protocol given in the Closure Supplement (Copy-time bound / Point~(6))), \( \frac{\chi_Y}{T_\star^2} = 0.145 \pm 0.010,\qquad \) \( \kappa_{\mathrm{eff}} = 0.1356 \pm 0.0714,\qquad \) \( C_\Lambda = 1.606 \pm 0.044 \), we obtain the Golden Relation \( m_S = C_\Lambda \sqrt{\kappa_{\mathrm{eff}}\,\chi_Y} \) and the prediction \( m_S = 58.5 \pm 15.6~\text{GeV},\qquad \) \( m_S \in [43,74]~\text{GeV}\ \text{(conservative)} \). We provide a minimal, fully analytic phenomenological consistency check of the Higgs-portal model in the vicinity of the Higgs resonance, using closed-form expressions for the Higgs invisible width and the spin-independent nucleon cross section. The mass prediction is conditional on the explicit benchmark intervals and on the stated matching assumptions; the copy--susceptibility exponent is universal in the variational sense above, while the overall normalisation entering the benchmark closure is calibrated using a diffusive benchmark class (a separate step, not used in the unconditional bound).
