Identity Theory: Thirty-Seven Fundamental Quantities from a Single Axiom with Zero Free Parameters

A candidate theory of everything is presented, built from a single axiom — thatmass, gravity, spacetime, and motion are identical, not four related quantitiesbut one thing. From this axiom and three measured inputs (σ_8 = 0.811, spatialflatness, and the CMB temperature), the framework derives thirty-sevenfundamental quantities spanning twenty-four orders of magnitude with zero freeparameters: the dimensionality of spacetime (3+1), the Standard Model gaugegroup (SU(3) × SU(2) × U(1)), Einstein's field equations, the Chern-Simonsaction, three coupling constants, the Weinberg angle, the fine structure number137, all three charged lepton masses, the neutrino mass, the quark mass ratio,the proton mass, the Higgs VEV, the W/Z/Higgs boson masses, the Higgs quarticcoupling, Planck's constant, the cosmological constant, the vacuum energy, theBorn rule, the uncertainty principle, the cosmic energy budget, and the BAOdistance scale. No other framework derives its own mathematical machinery (theCS action), its own field equations (EFE), its own gauge group, its own couplingconstants, AND its own particle masses from a single principle. The scope —from quantum foundations to particle physics to cosmology — with every derivedquantity matching observation to 0.02–6%, is what distinguishes this as a theoryof everything rather than a theory of one domain.The number of spatial dimensions is derived from knot stability (1-knots arepermanently stable only in 3D); the temporal dimension is derived as theHamiltonian evolution direction generated by the identity's canonical structure(Ξ ≡ [Â₁, Â₂] ≠ 0, the self-sustaining property called "the Jelly"). The gauge groupis derived as the exhaustive set of self-consistency requirements for selfreferencing geometry in 3D: directional consistency (SU(3)), orientationalconsistency (SU(2)), and closure consistency (U(1)). These are categoricallydistinct, forcing a product structure and predicting no proton decay, no fourthforce, and no magnetic monopoles. Coupling constants are derived from ChernSimons self-consistency: α_s = 1/8, α_w = 1/30, α_EM = 1/128, and sin²θ_W =30/128 = 0.234 (measured 0.231, +1.4%). The electron mass m_e = 0.484 MeV isderived from the Planck mass and coupling products; the muon mass from theNambu relation m_μ = m_e × (N_c/N_w) × 137 = 105.0 MeV (−0.61%); the taumass from the Koide coefficient Q = N_w/N_c = 2/3; the neutrino mass m_ν =m_e × α_wk_s = 0.021 eV (prediction: Σm_ν = 0.098 eV); the proton massm_p = μ_CS × α_s² = 960 MeV (+2.3%), with the cross-check m_p/v = α_s²/N_w²holding exactly. The quark mass ratio m_d/m_u = 2.156 is derived via runningtopology (measured 2.162, −0.3%). The Higgs VEV v = N_w² × μ_CS = 245.77GeV (−0.18%), the W boson mass 79.53 GeV (−1.05%), the Z boson mass 90.89GeV (−0.32%), and the Higgs mass M_H = v/N_w = 122.88 GeV (−1.77%) allfollow from derived integers. Planck's constant ℏ is derived from the fundamentalequation ρ_DE = ρ_Planck × (α_s α_w α_EM)137/5 with 0.02% precision,solving the cosmological constant problem computationally: the 10¹²⁰ ratiobetween Planck and vacuum energy densities equals (30720)27.4, with everyfactor derived. Einstein's field equations are derived directly from the CS actionon M³ plus the self-sustaining property Ξ, verified in three limits (Poisson,Schwarzschild, FRW), with Lovelock's theorem as an independent cross-checkconfirming uniqueness. Modified gravity is excluded as a falsifiable prediction.The cosmic energy budget emerges from baryonic kinetic energy accumulatedover cosmic time: dark matter (predicted 27.2%, observed 26.8%) and darkenergy (predicted 67.9%, observed 68.3%) are geometric residue of baryonicmotion, split by cosmic web dimensionality. The baryon fraction Ω_b = 0.0494 ispredicted from the intersection of two independent geometric constraints(Planck: 0.0493, +0.2%). Compared against DESI Data Release 2 baryon acousticoscillation measurements, the framework achieves χ² = 12.7 across thirteen datapoints versus ΛCDM's 38.9 — an improvement of Δχ² = −26.2 with zeroparameters fitted to BAO data. Galaxy rotation curves across 120 SPARCgalaxies favor cored profiles over cusped (Δχ² = 11,500 for Burkert over NFW).No dark matter particles, quintessence fields, or additional free parameters areintroduced.