Forward Modeling of H₀ Estimator Drift: The Mirage Operator and the Non-Existence of a Universal H₀

The Hubble tension (H₀ tension) can be formulated as an estimator-drift problem: it compares H₀ estimators inferred in finite domains under distinct observational procedures. The non-commutativity between dynamical evolution and inference operators established in Prevedello (2026, doi:10.5281/zenodo.18642415) implies that observational estimators do not directly recover the underlying dynamical rate. This work tests MRUV cosmology by constructing the complete forward operator mapping dynamics onto observables, including: (i) MRUV dynamics R(t), (ii) null geodesic propagation and observable redshift in a metric with temporal lapse A(t) and dimensionless photonic scale factor B(t) = R(t)/R_max, and (iii) finite-window inference through an estimator Π producing Ĥ(W). The redshift relation (1+z) = (A₀B₀)/(AₑBₑ) couples temporal lapse to expansion, generating a class of observational projections beyond standard assumptions. A minimal physical closure is imposed directly at the level of observables by requiring: (1) correct low-redshift distance scaling, and (2) minimal curvature of the luminosity distance D_L(z). This prevents spurious estimator drift induced by artificial curvature in the observable. Under this closure, forward modeling yields a drift coefficient β_pred = -7.23 ± 0.86 km/s/Mpc, in comparison with Pantheon+SH0ES observations β_obs = -9.8 ± 1.2 km/s/Mpc, corresponding to a difference Δβ = 2.57 km/s/Mpc and a tension of 1.7σ. In addition, we establish a general structural result implied by the operator formulation: there exists no scalar estimator of the Hubble parameter that remains invariant under changes in observational window or projection operator. The Hubble constant must therefore be interpreted as an operator-dependent and scale-dependent quantity rather than a universal constant. This dependence arises generically in any cosmological model with nonlinear luminosity distance, including ΛCDM. These results show that part of the observed H₀ tension can emerge from the structure of cosmological inference itself, while MRUV provides a concrete physical realization of this mechanism through forward modeling. This work operationalizes the Non-Commutativity Theorem (Prevedello 2026, doi:10.5281/zenodo.18642415) and completes the methodological closure initiated in Prevedello (2025, doi:10.5281/zenodo.17917734). It establishes both a concrete physical test (MRUV compatibility at 2σ level) and a general theoretical result (non-existence of universal H₀ as an operator invariant).