Frame Dragging with a Torsion Source: The Einstein-Cartan Gravitomagnetic Channel for Earth and the Sun

This paper isolates a single channel of Einstein-Cartan spin-torsion gravity: the gravitomagnetic (frame-dragging) term sourced by the intrinsic spin of a rotating body. A net spin density sets a gravitomagnetic precession scale Omega_T = 8 pi G s_net / c^2, evaluated for a rotating sphere under an explicit spin-density model (nucleons of number density n = rho/m_n, each of spin hbar/2, polarization fraction p) for Earth and the Sun, using the Aldred frame constant rho_A = 9.72e54 g/cm^3. Even at the unphysical full-alignment ceiling p = 1, and under an envelope construction that applies the interior scale undiluted to exterior measurements (the true exterior prediction is exactly the general-relativistic Lense-Thirring field, since torsion vanishes in vacuum), the correction is 2.11e-14 milliarcseconds per year for Earth - 14.5 orders of magnitude below the Gravity Probe B uncertainty (7.2 mas/yr on a 39.2 mas/yr signal) and 13.5 orders below the strongest claimed LARES/LAGEOS combined uncertainty - and 5.39e-13 milliarcseconds per century for the Sun, 13.0 orders of magnitude below the adopted 5 mas/cy planetary-ephemeris uncertainty on Mercury's perihelion longitude (solar Lense-Thirring signal 2.02 mas/cy). At the physical polarization (statistical fluctuation only), the corrections fall to 3.53e-40 mas/yr (Earth) and 1.57e-41 mas/cy (Sun), short of measurement by 40.3 and 41.5 orders of magnitude. Reaching even the p = 1 ceiling would require measurement precisions of 2.11e-14 mas/yr (Earth) and 5.39e-13 mas/cy (Mercury). AI-use disclosure: the computation and drafting of this manuscript were performed by Dave, an AI system operated by Aldred Industries, under the direction of the author of record, William Alexander Aldred, who has reviewed the manuscript and takes responsibility for its content.