The Curvature Relaxation Model: A Four-Paper Program for Geometric Cosmology Without the Dark Sector

A four-paper series presenting the Curvature Relaxation Model (CRM), a geometric framework that derives dark-matter phenomenology from scalar-curvature dynamics without postulating new particles. CORE-PAPERS Paper I: Game-Theoretic Foundation — Establishes the CRM through thermodynamic game theory (Jacobson tradition), deriving curvature saturation from Nash equilibrium between expansion and gravity. Paper II: MOND Emergence — Shows that Modified Newtonian Dynamics emerges as an effective background coupling from the running curvature parameter β ≈ 2.0, fitted to Pantheon+ and CMB data. Paper III: Lagrangian Formulation — Provides the covariant Lagrangian with Pöschl–Teller scalar potential, MCMC-fitted f(R)…