Non-Invariant Mass Estimators in Finite Observational Windows: A General Theorem and MRUV Realization in Ultra-Dark Galaxy CDG-2

Cosmological parameters and dynamical masses are not directly observed, but inferred through procedures defined over finite observational domains. Building on the MRUV cosmological framework introduced in Elimination of Dark Matter and Dark Energy: Geometric Derivation and Observational Validation of the Kinematic Crossing at z ≈ 0. 38 (Prevedello, 2025, Zenodo, https: //doi. org/10. 5281/zenodo. 17917734), the operator framework formalized in The Non-Commutativity Theorem between Dynamics and Inference in Cosmology (Prevedello, 2026, Zenodo, https: //doi. org/10. 5281/zenodo. 18642415), and its operational realization in Forward Modeling of H0 Estimator Drift: The Mirage Operator and the Non-Existence of a Universal H0 (Prevedello, 2026, Zenodo, https: //doi. org/10. 5281/zenodo. 18728744), this work elevates estimator dependence to a model-independent structural result. We formulate a general theorem demonstrating that, for any cosmology with nonlinear mapping from dynamics to observables, finite-window inference generically produces non-invariant estimators. If Ĥ (W) = ΠW (F) denotes an inferred Hubble estimator over window W, then in general Ĥ (W₁) ≠ Ĥ (W₂) for W₁ ≠ W₂, implying that no invariant scalar estimator exists independently of the observational window or inference operator. The same structure applies to inferred dynamical mass, showing that large apparent mass discrepancies can emerge as operator-dependent observables rather than being exclusively attributable to additional matter components. This is illustrated through the ultra-dark galaxy CDG-2 (Li et al. , 2025, https: //doi. org/10. 3847/2041-8213/adddab). Within MRUV cosmology, characterized by a universal acceleration scale Φ = 5. 57 × 10⁻¹⁰ m/s², we derive geometric amplification and predict Mdyn / M* ≈ 1660, matching observations within uncertainties without invoking non-baryonic matter. This theorem-and-realization structure yields falsifiable correlations between inferred mass discrepancy, local acceleration scale, and observational window choice. The model-independent result applies equally to ΛCDM, indicating that the Hubble tension and inferred mass discrepancies need not be uniquely attributed to underlying physical components, but can arise from the structure of cosmological inference itself. In extreme systems such as CDG-2, this framework reproduces discrepancies of the same magnitude as those observed (Mdyn / M ≈ 10³), without invoking non-baryonic matter.