Free Core Nutation: Inferring Core Flattening from the Resonance Period

This study computes the free core nutation 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: observed resonance period 430 sidereal days; effective core ellipticity required 0.0188; ellipticity from boundary shape alone 0.0064; period a shape-only model would give 1269 days; share that compliance and coupling must supply 66 percent. The standard geophysical account reproduces the measured behaviour of the nutation of the Earth 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. Nutation is the only observation that sounds the flattening of the core-mantle boundary directly, and the arithmetic here shows why: the resonance amplifies a boundary property of order a few parts in a thousand into a period measured in hundreds of days, giving geodesy a lever on a boundary no seismic phase samples as cleanly. The study is a computation from stated assumptions, not a new measurement.