Relational Mathematical Realism (RMR) proposes that physical reality emerges from a discrete 137-node registry partitioned as 81 (spatial) + 40 (surface) + 16 (gravitational). We develop the thermodynamic screening mechanism introduced in the RMR synthesis paper [3] into a self-contained predictive framework. A universal screening unit δ0 = 5/137, derived from the registry’s electromagnetic surface fraction, generates mass corrections across leptons, hadrons, and the fine-structure constant with zero fitted parameters. Key results: (i) α−1 = 137.035 996 versus CODATA 137.035 999 (error 3 × 10−6); (ii) mΛ0 /me = 2183.328 versus PDG 2183.327 (error 4 × 10−7, sub-keV on a GeV-scale mass); (iii) a strangeness screening integer Bs = V (K3)2 = 9 derived from the K3 ⊗ K3 product graph, yielding correct corrections for Λ0 and K+; (iv) a {9, 13, 17} strangeness ladder for Λ0, Ξ−, Ξ0 with step size 4, arising from K5 interface topology; (v) a charge-dependentovershoot theorem: corrections exceeding the 42 = 16 gravitational threshold are clipped by 4for charged particles, with three-particle confirmation (τ −, Ξ−, Ξ0). Eleven independent mass predictions are tabulated. A screened-angle ladder extends these results to dimensionless mixing observables: the effective leptonic weak mixing angle, the three PMNS angles, and the reactor angle are all approximated by δ0-corrections of quarter/half base states using multipliers from established graph integers, with no new parameters. Open sectors (meson bases, Ω− decuplet, Σ0 isospin mixing, and radiative corrections to the mixing angles) are characterized precisely andreserved for future work.