Mechanical Derivation of GP-B Precessions Based on Absolute Time Theory and Energy Equipartition

This paper presents a purely mechanical derivation of the gyroscope precessions (geodetic and frame-dragging effects) observed in the Gravity Probe B (GP-B) mission, utilizing the framework of Energy Conversion Field (ECF) theory. We demonstrate that the two orthogonal precessions share a highly symmetric mechanical origin governed by the Absolute Time Equation. Crucially, the 1/2 equipartition rule is not an ad hoc coefficient, but an intrinsic property of a mass's rest energy, fundamentally partitioning it into kinetic and potential components (mc²/2). By formulating the interaction between these intrinsic energy states and the gravitational field, we establish the principle of Energy-Phase Equivalence. We show that the ratio of the constraint energy pooled in the ECF to the system's absolute total energy directly dictates the geometric phase shift of the local reference frame (Γ = ΔE / [T.E.] = Ω / ω). Based on this strict mathematical equivalence, the framework deterministically yields theoretical precession values (6.6039 arcsec/yr for geodetic and 40.8 mas/yr for frame-dragging) that perfectly match the GP-B empirical data through explicit numerical verification.