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

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. 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) parameters, CMB Cℓ spectra, and S₈ predictions. Paper IV: Vector Sector and Galactic Dynamics — Extends the scalar sector by a massive Proca-type vector field (Daughter 2), derives the a₀ ≈ cH₀/(2π) relation, and tests against 175 SPARC galaxies. Version 6.0 changes (2026-03-13): Backward-impact revision (11 REV points across all papers), literature update (8 LIT-CRM points including Brodie 2026, DES Y6, Famaey & McGaugh 2012, mimetic gravity, Jacobson non-Riemannian 2026), soliton-ensemble UV completion candidate (Paper III), full EN/DE synchronization, duplicate bibitem fix (Paper I).