A Bound on the Time Variation of the Gravitational Constant from Lunar Laser Ranging in a Torsion-Regulated Frame

This paper computes the fractional time variation of G (Gdot over G) for the expansion history of the lunar orbit as tracked by lunar laser ranging within a torsion-regulated gravitational frame — Einstein-Cartan gravity with the density bound that follows from its spin-torsion term — and compares the result with the best published measurement. The relativistic prediction is 0 per year; the published value is 4e-13 plus or minus 9e-13 per year, a residual of 4e-13 per year (0.4444 standard deviations). Because torsion in this framework is sourced only by spin density and does not propagate, the predicted deviation from general relativity is set by the square root of the ratio of the system density to the bound density, giving a fractional deviation of 5.866e-28 and a correction of 5.866e-28 per year. The measurement bounds any fractional deviation at 2.2e-12 (two standard deviations), so the framework passes this test with a headroom factor of 3.75e+15. Stated plainly, the test is consistent with the framework but cannot distinguish it from general relativity; the implied lower bound on the density scale, 6.909e+26 kilograms per cubic metre, lies far below the framework's bound of 9.718e+57 kilograms per cubic metre. The study is computed from stated assumptions and published data; it is simulated, not measured.