The Emergence Canvas Model: The Unified Framework for Fundamental Physics — The Machine and the State

This is the complete and definitive edition of the theory. It contains the full derivation of the Standard Model—all gauge couplings, mixing angles, and fermion masses—from the eight primitives. Fundamental physics—the Standard Model and cosmology—has relied on twenty-five free parameters with no explanation for their values. This paper derives all of them from eight primitives and four pillars. The Canvas Model has zero free parameters within particle physics. Two boundary conditions—the age of the universe and its initial smoothness—specify the State. Everything else follows. What the theory derives from first principles: · Gauge couplings in closed form: g_1^2 : g_2^2 : g_3^2 = 1 : 2/3 : 2/\pi, matching data at sub-percent precision· CKM matrix: \lambda = 1/(2+3) = 1/5, with all four Wolfenstein parameters within 1\sigma· PMNS matrix: \theta_{13} = \arcsin(1/(3\sqrt{5})) = 8.57^\circ, matching the observed central value exactly· All quark, charged lepton, and neutrino masses from geometric overlaps and harmonic modes· Higgs vev: v = 245 GeV from the hierarchy formula· Higgs mass: m_H = 124.5 GeV from RG evolution· Cosmological constant: \Omega_\Lambda = 0.685 from the horizon information bound· Inflation: N_{\text{inf}} = e^4 \approx 55, n_s = 0.964, r \ll 0.01· Strong CP angle: \theta_{\text{QCD}} = 0 exactly by horizon topology· Born rule from threshold crossing statistics· Black hole entropy from voxel counting and the Einstein equations· Einstein field equations from lattice compression via Regge calculus· Gauge group SU(3)×SU(2)×U(1) from subspace dimensions· Three fermion generations from the eigenvectors of a single 3 \times 3 matrix All predictions emerge from five numbers: \alpha_0, \{1,2,3\}, and \pi. Structure: Part I (The Machine) tells the story from largest scales to smallest. Part II (The State) covers boundary conditions. Part III (Complete Derivation) is organized by sector: gauge, flavor, mass, neutrino, Higgs, cosmological, and quantum foundations. Fifty appendices contain the full mathematical proofs. The Canvas Model describes two things: the Machine (the timeless laws, zero free parameters) and the State (our particular universe, two boundary conditions). The Machine is complete. The State is now. Keywords: unified framework, canvas model, gauge coupling unification, fermion masses, CKM matrix, PMNS matrix, neutrino masses, cosmological constant, dark matter, inflation, strong CP problem, measurement problem, machine and state, emergence Note to Readers: Registered arXiv physicists in hep-th, hep-ph, or gr-qc who find this work valuable are invited to endorse it at: https://arxiv.org/auth/endorse?x=PUTIXH Contact: [e-mail]