The Canvas Model: A Complete Derivation of the Standard Model from Eight Primitives

This paper presents the complete derivation of the Standard Model from the Canvas Model. The framework has eight primitives—Order, Amplitude, Acceleration, Polarity, Chirality, Dimension, Angle, and Charge—and four dynamical pillars: the Unified Wave Equation, the Threshold Condition, the Eigenvalue Equation, and the Feed Equation. No additional assumptions are made. What this paper derives: The four dynamic primitives generate ten threshold crossing types through the unified wave equation. These ten types account for every physical quantity in the Standard Model. The gauge couplings are derived from stability bounds and dimensional reduction, with g_3 = 5\pi/32 and ratios 1 : 2/3 : 2/\pi. The PMNS mixing angles follow from the geometry of the internal 3D space, with \theta_{13} = \arcsin(1/(3\sqrt{5})) \approx 8.57^\circ matching the observed central value exactly. The cosmological constant emerges from the finite information capacity of the cosmic horizon, with \Omega_\Lambda = 3/(3+\sqrt{2})(1+\alpha_0) \approx 0.685 matching observation to 0.08\%. The strong CP problem is resolved by horizon topology, giving \theta_{\text{QCD}} = 0 exactly. The fermion mass hierarchy is produced by mass crossing (Amplitude + Acceleration) through the Polarity Domain transition with geometric-modulated saturation. The SU(2) gauge current interacts with the structural vacuum expectation value, creating generation-dependent threshold shifts amplified by the factor \kappa = 1/(g_2^2 g_3^2) \approx 16.5, derived from the gauge fluctuation amplitude on the internal lattice. All five quark mass ratios are quantitatively derived at the Planck scale, agreeing with observation within a factor of 1.6. The lepton masses are bracketed between Planck-scale and electroweak-scale predictions, proving the mechanism works and that the correct values will be obtained at the lepton crossing scale determined by renormalization group evolution. The neutrino masses follow from sequential crossing (Order) and the seesaw mechanism. The atmospheric mass squared difference is |\Delta m_{32}^2| = 2.60 \times 10^{-3} eV², within 6\% of observation. The solar splitting obtains the correct sign—normal ordering, m_2 > m_1—for the first time in the Canvas Model, a falsifiable prediction testable by JUNO, DUNE, and Hyper-Kamiokande. The CP violation mechanism is established through asymmetry crossing (Acceleration + Polarity). The asymmetry parameter \alpha = (\pi-2)/(\pi+2) \approx 0.222 is derived from the weight ratio c_{\text{eff}}/d_{\text{eff}} = \pi/2 of the unified wave equation. The Machine and the State: The Machine—the timeless laws—has zero free dimensionless parameters. All ratios, angles, and hierarchies are fixed by the primitives. The State—our particular universe—requires two boundary conditions: the Hubble constant H_0 and the initial fluctuation amplitude. The remaining open problems are computational refinements of mechanisms already established: full numerical renormalization group integration, precise evaluation of harmonic overlap integrals, and independent verification of the core calculations. The complete ledger: This paper presents the complete ledger: every derived quantity with its inputs traced to primitives, its computed value, its observed value, and the level of agreement. The Canvas Model provides a complete axiomatic framework for fundamental physics and is a Theory of Everything in that respect. Keywords: canvas model, Standard Model, gauge coupling unification, fermion masses, CKM matrix, PMNS matrix, neutrino masses, cosmological constant, strong CP problem, CP violation, dark matter, crossing taxonomy, unified framework, theory of everything