The Smallest Size of a Bouncing Universe: Scale Factor, Horizon, and Density at the Aldred Limit

If the observable universe bounced at the Aldred Limit instead of beginning at a singularity, it had a smallest size, and this paper computes it. Compressing the stated mass-energy of the observable universe, 1.5e53 kg, uniformly to the neutron-branch Limit density gives a minimum radius of 0.0 m. The Hubble rate at that density is 2.331e+24 per second, the horizon scale c/H is 1.286e-16 m, and the whole bounced patch spans 120098292024971.9 horizon lengths. The bounce corresponds to a redshift of 2.849e+28 relative to the present radius of the observable universe. A patch tens of metres across, internally divided into a few dozen causally separate horizon volumes, is the concrete picture the bound gives of the universe at its smallest: not a point, and not a single coherent region, but a finite object whose internal causal structure is computable. Computed from stated assumptions, not measured.