A Travel-Time Test of Inner-Core Differential Rotation

This study computes inner-core differential rotation from stated inputs and places the result against both the published observational value and the density ceiling of Einstein-Cartan torsion gravity, in which spin-sourced torsion caps the effective density of neutron matter near 9.72e57 kilograms per cubic metre. The computation gives: travel-time drift at 0.3 degrees per year 0.03 s over 20 years; travel-time drift at 0.1 degrees per year 0.01 s over 20 years; equatorial surface speed at 0.1 degrees per year 2131 m per year; smallest rate resolved at 0.02 s over 20 years 0.172 degrees per year. The standard geophysical account reproduces the measured behaviour of the solid inner core within the uncertainty of its inputs, and the largest correction the ceiling could contribute at terrestrial densities is far below the precision of the observations, so the measurement is consistent with the frame while also naming the threshold at which it would cease to be. The history of this measurement is a cautionary example of a signal at the edge of resolution: the early large rates and the later small ones differ mainly in how source errors were handled, and stating the travel-time arithmetic plainly shows how large a rotation the doublet data can still hide. The study is a computation from stated assumptions, not a new measurement.