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

The Curvature Relaxation Model (CRM) replaces dark energy with a geometric curvature return potential and embeds modified gravity within the Horndeski/f (R) framework. This deposit contains four papers presenting a complete theoretical program: Paper I establishes the game-theoretic foundation and validates the CRM against Pantheon+ supernovae (Delta chi2 = -12. 2 vs. LCDM). Paper II extends the framework to a baryon-only universe with MOND unification, achieving joint SN+CMB+BAO compatibility (Delta chi2 = -5. 5). Paper III provides the Lagrangian underpinning (R + gamma R2) with full hiclass CMB validation, yielding Delta chi2 = -3. 7 vs. LCDM on Planck 2018 data (alphaM0 = 0. 0011, 1. 76 sigma detection). Paper IV introduces the vector sector for galactic MOND dynamics and tests against the full SPARC database (171 galaxies), deriving the MOND scale a0 = cH0/ (2pi) from first principles (13% discrepancy, 0. 66 sigma). Analysis code available at https: //github. com/lukisch/cfm-cosmology.