The Spin Density at the Bound: Counting Aligned Angular Momentum at the Aldred Limit

The Aldred Limit is a statement about spin density, and this paper counts the spins. At the bound density the neutron number density is 5.802e+84 per cubic metre, giving an incoherent spin density of 3.059e+50 in SI units. A 1.4 solar mass bounced core contains 1.662e+57 neutrons. If their spins were fully aligned the core would carry a total angular momentum of 8.764e+22 kg square metres per second; with random orientations the resultant is only 2.150e-06, smaller by a factor 4.077e+28. That factor, the square root of the spin count, is the quantitative measure of how much angular momentum the incoherent prescription leaves on the table, and it is why the torsion source is governed by the local squared spin density rather than by any net rotation of the core. The counting also separates two ideas often confused: the core's net spin, which is negligible, and its spin density, which is what reaches the bound. Computed from stated assumptions, not measured.