The Einstein Radius of Abell 1689 in the Torsion-Regulated Frame: A Computed Correction in Milliarcseconds

This paper computes the change that the torsion-regulated Einstein-Cartan framework, organised by the Aldred Limit, predicts for Einstein radius of Abell 1689, whose published value is about 45 arcseconds. The density of the system, estimated from its published properties by the estimator stated in the Methods, is 8.56e-22 kilograms per cubic metre. At that density the fractional correction to the effective gravitating density is 8.81e-80 on the neutron branch and 2.98e-73 on the electron branch, against a measurement precision of 5 per cent. The predicted change is therefore smaller than the precision by a factor of 5.67e+77 on the neutron branch. Inverting the comparison, the existing agreement excludes carrier masses only below 1.25e-30 electronvolts, and the system would need a density of 9.72e+55 kilograms per cubic metre for the correction to reach one per cent. The result is a null result, stated plainly: this observable neither supports nor meaningfully constrains the framework, and the framework contributes nothing to the interpretation of this system beyond standard gravity. Computed from stated assumptions and published data; not a new measurement.