The Timeless Quanta (TQ) framework models subatomic structure through a locked hybrid Gaussian–exponential shell with collapse radius rc = 0.447 fm fixed by Komar-energy equivalence, onset width σ = 0.10 fm, and relaxation length L = 1.43 fm. This paper identifies rc as the physical Ricci-onset handoff surface between microscopic TQ curvature activation and macroscopic Time-Dilation Geometry (TDG) normalization. A minimal first-order matching law on the dimensionless Ricci-active amplitude yields the scale-adaptive exponent β_TQ-TDG = 1 − σ/L = 0.93007, distinct from the null value β = 1 of the pure exponential tail. The result is verified numerically across Gaussian, top-hat, and exponential coarse-graining kernels. The derived exponent provides a sharp, falsifiable bridge prediction for cross-scale baryonic-curvature tests in galactic dynamics, weak lensing, and cosmological observables.
Publication Date: 2026-06-23