The Brown Dwarf Boundary at Planetary Masses: Central Density of Substellar Objects Against the Bound

This paper computes where 13 Jupiter-mass centre sits relative to the density bound that arises in Einstein-Cartan gravity when the spin of fermionic matter sources torsion. The bound on the neutron branch is 9.72e+57 kilograms per cubic metre, and on the electron branch 2.87e+51 kilograms per cubic metre. The primary system examined, 13 Jupiter-mass centre, has a density of 1.00e+06 kilograms per cubic metre, which is a fraction 1.03e-52 of the neutron-branch bound — a margin of 52.0 orders of magnitude. The fractional correction that the bound makes to the effective density, and hence to structure quantities built from it, is that same ratio to leading order. Further systems examined here are 13 Jupiter-mass centre at 1.00e+06 kilograms per cubic metre; 70 Jupiter-mass centre at 3.00e+06 kilograms per cubic metre; Jupiter centre at 2.50e+04 kilograms per cubic metre. The conclusion is stated plainly: at these densities the correction is present in the equations and absent from every digit that observation or modelling can reach, and this paper quantifies that absence system by system rather than asserting it. The study is computed from stated assumptions; it is not a measurement.