Shapiro Delay in PSR J1614-2230 and the Two-Solar-Mass Clock as a Frame Test

This paper computes the Shapiro shape parameter s for the millisecond pulsar PSR J1614-2230 with its white-dwarf companion 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 0.9999 dimensionless; the published value is 0.9999 plus or minus 3e-05 dimensionless, a residual of -5.076e-06 dimensionless (-0.1692 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 8.487e-21 and a correction of 8.487e-21 dimensionless. The measurement bounds any fractional deviation at 6.508e-05 (two standard deviations), so the framework passes this test with a headroom factor of 7.668e+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, 1.653e+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.