Does Fundamental Physics Follow from Pure Geometry?

We derive, compute, or identify all dimensionless constants and the dynamical rules of the Standard Model — coupling constants, particle masses, mixing parameters, the gauge group, the Lagrangian, and the Feynman rules — from the geometry and representation theory of a single, scale-invariant object with zero free parameters. Results are labeled as derived (from the character table alone), computed (from transfer matrix eigenvalues), or pattern-matched (numerically identified, awaiting derivation from the boundary transfer matrix). The fine structure constant is obtained as α^-1 = 20φ⁴ − (3+5√5) /308 = 137. 035999260 (0. 4 ppb from the rubidium measurement) ; its running to the Z mass gives 1/α (MZ) = 128. 055 (0. 08%) from one class algebra coefficient and one logarithm. Thirteen particle masses spanning 22 orders of magnitude from the electron to the Planck mass are derived with an average error of 0. 6%. All four CKM quark mixing parameters emerge from pentagonal geometry, including the CP-violating phase δ = 2π/5 = 72° (1. 4%). The Weinberg angle is sin² (θW) = 3/13 (0. 037%), the reactor neutrino angle sin² (θ₁₃) = (5−2√5) /24 (0. 03%), and the cosmological constant is ρP/ρDE = 60^69 = 10^122. 7. The gauge group SU (3) ×SU (2) ×U (1) emerges from the conjugacy class structure, with 8 gluons decomposing geometrically as 5 bulk + 3 boundary modes. The dark matter fraction is dim (χ₄) ²/|A₅| = 26. 7%. A complete dark sector spectrum is computed, with a dark proton at 977 MeV and dark confinement 26% above QCD. The Thomson scattering angular distribution (1+cos²θ) is derived exactly (10^-16) from the lattice Green's function and the 5-design property, with no input from QED. The Born rule is proved, not postulated, from Schur orthogonality and Gleason's theorem.