Cosmological Redshift as Coherence-Dependent Propagation

The Hubble tension---the $4$--$6\sigma$ discrepancy between early-universe (CMB/BAO) and late-universe (Cepheid/SNIa) determinations of $H_0$---remains unexplained within $\Lambda$CDM. We propose a candidate mechanism within Lambda Convergence Universal Field Theory (LUFT), in which time is emergent and the vacuum is characterized by a coherence-dependent propagation bound. Earlier versions of this paper presented the mechanism as derived, via $c^2 = A/B \propto \langle\Xi\rangle^{-1}$ from the scalings $A \propto v_{\mathrm{eff}}$, $B \propto v_{\mathrm{eff}}^3$ of the Gaussian partition function on $T^3$. That reading is withdrawn (status notice below): per Spine v2.13.0 the quadrature ratio $A/B$ carries no kinematic content ($\mathfrak{c}^2$ is carried by the dispersion route), and a direct truncated-metric measurement (Spine v2.12.0) finds $A \propto v_{\mathrm{eff}}^{3.1}$, not $v_{\mathrm{eff}}^{1}$. The central relation of this paper, $\kappa \propto \langle\Xi\rangle^{-1}$ (Hypothesis $H_\Xi$), is therefore a hypothesis without Layer-0 anchor, not a mean-field consequence of the axioms. Conditional on that hypothesis, cosmological redshift is reinterpreted not as kinematic expansion but as adiabatic frequency renormalization induced by coherence degradation along the propagation path. The redshift relation becomes $1 + z_\kappa = [\kappa(\lambda_{\mathrm{obs}})/\kappa(\lambda_{\mathrm{emit}})]^{1/2}$, where $\lambda = \Xi/\Xi_{\max}$ is the coherence state variable. Non-linear $\kappa(\lambda)$ evolution produces epoch-dependent effective Hubble parameters: early-universe probes (high coherence, low $\kappa$) yield lower inferred $H_0$ than late-universe probes (low coherence, high $\kappa$), which would resolve the observed tension without dark energy. Scale separation ensures local Doppler measurements remain valid: impedance drift is negligible over distances $\lesssim 100$ Mpc. The same mechanism predicts $\Delta\alpha_{\mathrm{EM}}/\alpha_{\mathrm{EM}} \approx 0$, consistent with observations. The vacuum remains in a single broken phase for all coherence couplings $x \geq 0$: the SSB minimum persists and deepens monotonically, with no phase transition or restored symmetry (Spine v2.1.0). A self-consistent treatment of the propagator at the shifted vacuum replaces the bare scaling $(1+2x)^{-1}$ with a gap equation $(u-1)(3u-1) = 4x$, yielding the self-consistent kernel $u_{\mathrm{sc}}(x) = (2 + \sqrt{1+12x})/3$; this algebra is internally consistent and survives on its own merits. It eliminates the spurious critical point at $x = 1/2$ and calibrates the present-epoch coherence parameter $x_0 \approx 0.109$ from the observed Hubble ratio --- a one-parameter fit to the tension, not a prediction of it, and (per Spine v2.13.0) a calibration without Layer-0 anchor. Under the $x(z)$ ansatz the implied 17.3\ \vspace{0.3cm} Keywords: Hubble tension, Cosmological redshift, Lambda Convergence Universal Field Theory, Coherence degradation, Emergent time, Pre-metric field theory, Vacuum structure, Self-consistent kernel, Gap equation Version note (v3.4, June 2026): claim-status correction, no content rebuild. The earlier presentation "derived via c2 = A/B" is withdrawn (spine v2.13.0: A/B is a quadrature ratio with no kinematic content; direct measurement gives A scaling as v_eff^3.1, not v_eff^1). The central relation kappa proportional to 1/Xi is now a hypothesis without Layer-0 anchor; x0 ≈ 0.109 is a one-parameter calibration, not a prediction. A binding status notice precedes the paper; a rebuild is deliberately deferred.