Relational Distinguishability Framework II: Loop Closure, Cosmological Constant, Spin-Statistics, and Standard Model Structure

We extend the Relational Distinguishability Framework (RDF) to cosmological and particle-physics scales. Eight results are established, including: (i) the proof of a closed scale loop with period Lambda_c = 280.6; (ii) the derivation of the cosmological constant Lambda ~ 1.6e-52 m^-2; (iii) the derivation of the spin-statistics theorem from loop closure requirements; and (iv) the identification of SU(3)xSU(2)xU(1) as the unique rank-4 anomaly-free gauge group compatible with the framework's rank bounds. We also provide a mass formula for the Standard Model hierarchy and predictions for CMB log-periodic oscillations.