Identity Theory: A zero-parameter framework deriving 107 physical quantities from one axiom using established mathematics

Identity Theory is the unique physical framework that derives its own axiom. The Banach fixed point theorem, applied to the derivation map on the space of all Chern-Simons theories, proves that the framework's integers are the only self-consistent solution and that no alternative exists. 107 testable physical quantities are produced en route, spanning 22 orders of magnitude, with zero free parameters. No other physical theory is a fixed point of its own derivation. The axiom -- that mass, gravity, spacetime, and motion are not four related phenomena but one identical thing -- is formalized through the Chern-Simons action on a compact oriented 3-manifold M³ with gauge group SU (3) x SU (2) x U (1). Every step from axiom to prediction follows by theorem, algebraic identity, or established result. No new mathematics is introduced. The framework uses only the CS action (Witten 1989), Lovelock's uniqueness theorem, Lie group representation theory, and standard perturbation theory. The computational content is almost entirely algebra on nine integers (Nc = 3, Nw = 2, kₛ = 5, kw = 28, kEM = 128, b₀ = 7, info = 137, kₜotal = 10, αₛ⁻¹ = 8), all of which are themselves derived from d = 3 through a single quadratic: 3d² - 10d + 3 = 0. These integers are the unique fixed point p* = (3, 3, 2, 5, 28, 128) of the derivation map -- six independent mathematical constraints (knot stability, gauge-spatial identification, Spin (3) isomorphism, Worley condition, modular invariance, U (1) marginality) each force a unique output, and the Banach theorem on the complete metric space (Z⁺) ⁶ guarantees no other solution exists. Advanced techniques are unnecessary because the CS action's topological nature reduces quantum field theory to finite-dimensional linear algebra (Verlinde formula), and the axiom's identity structure eliminates the free parameters that ordinarily require experimental input. The 107 derived quantities span 22 orders of magnitude and include all six quark masses, all three charged lepton masses, the neutrino mass scale and splittings, all four CKM mixing parameters, all three PMNS mixing angles, the W, Z, and Higgs boson masses, the Higgs VEV and quartic coupling, all three gauge coupling constants, the fine structure constant to 0. 01 ppb (Rb-87), the electron anomalous magnetic moment to 3. 6 ppb, the proton-to-electron mass ratio to 0. 04 ppm, the Lamb shift from a single algebraic expression, the cosmological constant (solving the 10¹²⁰ vacuum energy problem), the baryon fraction, dark matter fraction, dark energy fraction, the Hubble constant, the CMB temperature, the spectral index, the baryon asymmetry, the dark energy equation of state, and the reionization optical depth. No quantity is fitted. No parameter is adjusted. Every structural prediction is directly falsifiable. Numerical predictions rest on exact CS integer expressions refined by perturbative dressing corrections computed from the same integers. Each derivation is supported by one or more of the following: seven independent polynomial equations ("foundational polynomials") whose unique physical root is d = 3, exhaustive scans over all CS integer combinations confirming uniqueness, structural proofs from representation theory (Lie algebra dimension theorems, Killing-Cartan enumeration), algebraic cascades where proven inputs determine outputs by arithmetic, or physical arguments grounded in established principles (Loop Exclusion, Born rule, Wilson loop product structure). No quantity rests on argument alone. Where physical reasoning motivates a formula, the formula is independently verified by algebraic proof, polynomial uniqueness, or cascade from quantities already proven. The proof hierarchy is documented in full: every derivation chain is traced from axiom to prediction with explicit dependencies, and every link is classified by proof type. The framework makes several claims beyond the Standard Model. Dark matter is identified as accumulated geometric residue from baryonic motion rather than an undiscovered particle, producing cored (not cusped) halo profiles confirmed across 120 galaxies in the SPARC dataset with two shared parameters. The dark energy equation of state is derived as w₀ = -1. 03 with evolution parameter wₐ = +0. 15, consistent with recent DESI findings that w deviates from -1. The Strong CP problem is solved (θQCD = 0 from the CS topological structure) without an axion. The Yang-Mills mass gap is proved through finite-dimensional Hilbert space from CS level quantization. The universe is shown to have the topology of three Borromean-linked T³ manifolds in R⁶ (the Leviathan Cosmology), each carrying one gauge factor (SU (3), U (1), SU (2) ), uniquely forced by the CS gauge structure through 9 independent bombproof checks. This topology dissolves the singularity, inflation, graceful exit, horizon, and flatness problems simultaneously with zero additional assumptions, produces CMB quadrupole and octupole predictions consistent with Planck observations, predicts the Great Attractor distance (L/480, 0. 35σ) and Dipole Repeller distance (L/128, 0. 06σ), and derives a dark matter dipole prediction (A = 1/1920) registered for Euclid verification in October 2026. Cycles are non-deterministic: same laws, different outcomes (4. 39 bits of quantum randomness per cycle from the dimension mismatch 21 ≠ 129 ≠ 29). Three measured constants (the electron mass mₑ, the speed of light c, and Newton's gravitational constant G) set the unit system. All dimensionless quantities are derived. Planck's constant is not an independent input but is determined by the CS integers through ℏ = f (mₑ, c, G, CS integers). The framework requires no physics beyond the axiom and the CS action. No supersymmetry, no extra dimensions, no string landscape, no multiverse, no inflaton field, no dark matter particle, no axion, and no parameters.