Identity Theory: A Single-Axiom Framework Deriving Cosmic Composition, BAO Distances, Coupling Constants, and Particle Masses with Zero Free Parameters

A framework built from a single axiom — that mass, gravity, spacetime, andmotion are identical, not four related quantities but one thing — is shown toderive twelve or more fundamental quantities spanning twenty-two orders ofmagnitude with zero free parameters. The cosmic energy budget emerges frombaryonic kinetic energy accumulated over cosmic time: dark matter (predicted27. 2%, observed 26. 8%) and dark energy (predicted 67. 9%, observed 68. 3%) aregeometric residue of baryonic motion, split by cosmic web dimensionality. Thebaryon fraction Ωb = 0. 0494 is predicted from the intersection of twoindependent geometric constraints (Planck: 0. 0493, deviation +0. 2%). Comparedagainst DESI Data Release 2 baryon acoustic oscillation measurements, theframework achieves χ² = 12. 7 across thirteen data points in seven redshift bins, versus ΛCDM's χ² = 38. 9 — an improvement of Δχ² = −26. 2 with zeroparameters fitted to BAO data. The framework's sound horizon rₛ = 153. 4 Mpcand Hubble constant H₀ = 66. 6 km/s/Mpc are both axiom-derived predictions. Coupling constants are derived from Chern-Simons self-consistency: αₛ = 1/8from central charge matching in SU (3), αw = 1/30 from operator marginality inSU (2), αEM = 1/128 from U (1) marginality, and sin²θW = 30/128 = 0. 234 (measured 0. 231, +1. 4%). The electron mass mₑ = 0. 484 MeV is derived fromPlanck mass and coupling products (measured 0. 511 MeV, −5. 3%). The quarkmass ratio md/mᵤ = 2. 156 is derived via running topology to 0. 3% precision (measured 2. 162). The fine structure constant's famous value 137 = kw × kₛ −Nc emerges from the same topological integers, and Planck's constant ℏ isderived from classical quantities with −2. 4% deviation. Einstein's field equationsare derived uniquely from the axiom via Lovelock's theorem, with modifiedgravity excluded as a falsifiable prediction. Galaxy rotation curves across 120SPARC galaxies favor cored profiles over cusped (Δχ² = 11, 500 for Burkert overNFW) as the framework predicts. No dark matter particles, quintessence fields, or additional free parameters are introduced.