Geometric Amplification of Anomalous Gravitomagnetic Coupling

The anomalous gravitomagnetic signals reported by Tajmar et al. (2006–2009) in rotating superconductor experiments remain unexplained within the standard framework of linearized general relativity. The measured coupling factors exceed the predictions of classical Lense-Thirring frame-dragging by approximately 19 orders of magnitude, suggesting either systematic artifacts or an anomalous amplification mechanism — possibly related to Cooper-pair coherence in the superconducting state. This paper introduces a previously unexplored dimension of analysis: the geometry of the rotating source. The Tajmar experiments employed flat cylindrical rings — a configuration that, within the ABÏON geometric framework (Bricio 2026a, 2026b), represents the least efficient topology for gravitomagnetic field generation. We apply the ABÏON formalism to quantify the geometric amplification factor of the Tajmar configuration (F_geo ≈ 1.0), and predict the signal enhancement achievable by replacing the flat ring with an optimized hyperboloid-paraboloid topology incorporating helical (Archimedes screw) threading. Our analysis shows that an optimized source geometry at the same scale, mass, and angular velocity as the Tajmar apparatus would produce a rotational gravitomagnetic signal approximately 25 times stronger than the flat ring configuration — a conservative estimate that accounts only for the geometric factor F_geo and the Anti-Venturi momentum concentration (Scenario A). Including coherent helical interference raises the gain to ~49× (Scenario B). Additional amplification mechanisms inherent to the ABÏON topology — gravitomagnetic cavity resonance between the double shells, Meissner screening current organization, phased array coherence, and superfluid helium entrainment — extend the predicted gain range to ~244× (Scenario C) and potentially ~2,100× at the theoretical maximum (Scenario D). We propose a specific experimental design — the Mini-ABÏON — that would test these predictions through systematic parameter sweeps using existing cryogenic and accelerometer technology. Even the most conservative scenario predicts a signal-to-noise ratio of ~240:1, transforming the measurement from marginal detection to unambiguous laboratory demonstration. Keywords: gravitomagnetism, frame-dragging, rotating superconductors, Tajmar effect, Cooper-pair amplification, topology optimization, ABÏON metric