Microscopic Framework for Anomalous Gravitomagnetic Coupling in Rotating Superconductors from Ginzburg-Landau Theory in Curved Spacetime

We present a microscopic-level framework for understanding the anomalous gravitomagnetic coupling reported by Tajmar et al. in rotating superconductors. The measured gravitomagnetic-to-angular-velocity ratio chi = B_g/omega is many orders of magnitude larger than the standard far-field Kerr prediction for a laboratory-scale rotating body. Building on the De Matos-Beck phenomenological model, we formulate the Coherent Vacuum Coupling Hypothesis (CVCH), in which the local gravitationally active vacuum energy density associated with a superconducting condensate acts as an effective gravitomagnetic source. Using the Ginzburg-Landau formalism in curved spacetime, with vierbein and spin-connection methods applied to an effective Kerr-like metric generated by the London moment of a rotating superconductor, we motivate the coupling chi = (3/2) rho_vac(T_c) / rho_vac^(Lambda). The framework identifies the T_c^4 ln^4(3) scaling of the local vacuum energy density and derives the numerical factor 3/2 within the central coupling ansatz from the w = -1 equation of state of the condensate. The coupling step itself is stated explicitly as a physically motivated conjecture rather than a closed derivation from BCS theory alone. For niobium, the model gives chi_Nb approximately 2.23e-4, consistent with the reported Tajmar range. It predicts a much stronger effect in MgB2, no anomalous signal in YBCO, and a sharp crossover near T_c = 90.1 K, with Bi-2212 lying below the crossover. The paper proposes falsifiable experimental tests, including a T_c crossing sweep, MgB2 torsion-pendulum measurements, and Bi-2212/YBCO comparison experiments.