The Complete Parameter Spectrum: How Five Numbers Generate All of Fundamental Physics

[SUPERSEDES]: One Number: How \alpha_0 = 1/\ln(I_{\text{max}}) Generates All of Physics The Standard Model of particle physics has nineteen free parameters. Cosmology adds at least six more. Together, these twenty-five numbers encode all known physics, spanning thirty orders of magnitude from the cosmological constant to the top quark mass. No existing theory explains more than a handful from first principles. This paper demonstrates that all physical parameters are generated by five fundamental numbers: the fundamental coupling \alpha_0 \approx 1/140 (determined by the information capacity of the observable universe), the integers \{1,2,3\} (the dimensions of the gauge subspaces of the internal 3D space), and the number \pi (the fundamental angle between orthogonal spatial axes). What the paper contains: The gauge couplings are derived in closed form, with ratios 1 : 2/3 : 2/\pi and absolute values fixed by the self-consistency of dimensional reduction. The CKM matrix follows from the sum of gauge subspace dimensions, with the Wolfenstein parameter \lambda = 1/5. The PMNS matrix is derived from the same principle, with the (1,3) angle \theta_{13} = \arcsin(1/(3\sqrt{5})) matching the observed central value exactly. The fermion mass spectrum is generated by an exponential Yukawa function derived from threshold crossing dynamics, reducing nine independent Yukawa couplings to one computed parameter. The electroweak scale is derived from the balance of threshold and information pressures, yielding v = 245 GeV. The cosmological constant is \Omega_\Lambda = 0.685, matching observation within 0.08\%. The strong CP angle is zero exactly. The inflationary spectral index is n_s = 0.964. The dark matter candidate is a Planck-mass black hole remnant. Why this matters: The Standard Model contains twenty-five free parameters with no explanation for their values. The canvas model reduces these to five fundamental numbers, each with a clear physical origin in the primitives. The Machine has zero free dimensionless parameters. The State has two boundary conditions (H_0, \Omega_{\text{DM}}). The universe is not described by twenty-five arbitrary numbers. It is described by five numbers. The canvas model explains not just what the parameters are, but why they are what they are. All derivations are presented with full mathematical rigor. All predictions are compared with experimental data. The agreement spans thirty orders of magnitude. Keywords: canvas model, parameter spectrum, gauge couplings, CKM matrix, PMNS matrix, fermion masses, Higgs mechanism, cosmological constant, inflation, strong CP, dark matter, five fundamental numbers, \{1,2,3\}, \pi, \alpha_0