Two Parameter-Free Predictions of the U-Cell Model: A Multi-Scale Consistency Test and the Two Characteristic Halo Radii

The U-Cell Model (UCM) derives gravity, dark matter, and cosmological expansion from a single substrate dispersion relation without free parameters. This record contains two companion papers. Paper 1 compiles four independent parameter-free UCM predictions — rotation curves (median chi²=0. 73 for 150 SPARC galaxies), the MDAR acceleration scale (0. 5% agreement with McGaugh et al. 2016), the local dark matter density (0. 1 sigma from Gaia/PDG), and the Milky Way virial radius (5% agreement with Gaia satellite kinematics) — all controlled by the single constant fcold = sqrt (2-pi/2). Paper 2 derives two physically distinct characteristic radii for every UCM halo: r₂00 (the conventional virial radius) and rᵥirial (the Euler junction radius), with a universal ratio rᵥirial/r₂00 = fcold*sqrt (150) ≈ 8. 02 independent of galaxy mass. Between these radii the halo maintains an isothermal r^-2 profile containing 88% of the total halo mass, producing a weak-lensing excess relative to NFW at r > r₂00. Both results are directly testable with Euclid DR1 (October 2026).