We introduce τ_A ≈ 0.63337052, a new mathematical constant defined as the asymptotic ratio of factorial orbit norms in the ring of integers of K = ℚ(ρ), where ρ is the real root of x³ − x − 1 = 0 (discriminant Δ = −23). Two equivalent representations are established: an exact rational infinite product (native to the Rational Worlds framework, no limits required) and an analytic formula via the Gamma function evaluated at the three roots of the generating polynomial. The constant is numerically verified to 15 significant figures and does not appear in prior literature. We then demonstrate that τ_A is the arithmetic density of the Structured Vacuum V₂₃ relative to a flat cubic lattice, and derive the Hubble constant H₀ = 70.20 km/s/Mpc from first principles — without free parameters — obtaining a value that falls between the Planck/CMB measurement (67.4) and the SH0ES/Cepheid measurement (73.0), proposing a geometric resolution to the Hubble tension.