(HEP format) A Unified Framework for Fundamental Physics from Eight Primitives

This paper presents a complete unified framework for fundamental physics derived from eight primitives and four core equations. The framework is based on a single mechanism—wave intersection above a critical threshold on a pre-geometric canvas—and contains zero free dimensionless parameters in its laws. Every result traces back to a specific subset of the axioms. The eight primitives—Order, Amplitude, Acceleration, Polarity, Chirality, Dimension, Angle, and Charge—are stated as axioms. The four pillars—the Unified Wave Equation, the Threshold Condition, the Eigenvalue Equation, and the Feed Equation—govern their interactions. From these, we derive the dimensionality of space (d=3), the orthogonality of spatial axes (θ=π/2), the Einstein field equations via Regge calculus with O(L²) convergence, the Schrödinger equation, the Born rule, the resolution of the measurement problem, and the Standard Model gauge group SU(3)×SU(2)×U(1). What this paper derives: The framework predicts exactly three fermion generations as the eigenvectors of a 3×3 threshold tensor on the internal coupling space. The gauge couplings are derived in closed form: g₁² = 25π³/2048, g₂² = 25π³/3072, g₃² = 25π²/1024, with ratios 1 : 2/3 : 2/π. The CKM and PMNS mixing matrices follow from the gauge subspace dimensions {1,2,3}, with λ_CKM = 1/5, θ₁₂^PMNS = 1/√3, θ₂₃^PMNS = π/4, and θ₁₃^PMNS = arcsin(1/(3√5)) ≈ 8.57°, matching the observed central value exactly. All nine charged fermion masses are computed from a single Yukawa formula with harmonic modes selected by a universal free energy functional. The electroweak scale emerges from the balance of threshold pressure and information bound pressure: v = 245 GeV. The cosmological constant is derived from the geometric subspace dimensions and the horizon information bound: ΩΛ = 0.685, matching the observed value to within 0.08%. The baryon asymmetry traces directly to the π/2 waveform asymmetry of the Unified Wave Equation: η ~ 10⁻⁹. The strong CP problem is resolved by the topology of the cosmic horizon: θ_QCD = 0 exactly. CMB observables are predicted: n_s ≈ 0.964, r ≪ 0.01. The framework has zero free dimensionless parameters in its laws and two boundary conditions—the age of the universe (H₀) and the initial fluctuation amplitude (Ω_DM)—that specify the state of our particular universe. The central falsifiable prediction is a universal waveform asymmetry T_rise/T_fall = π/2 in bound states formed by wave intersection, verified in 3+1D numerical simulation. Complete derivations are provided in the appendices. Why this matters: The Standard Model of particle physics contains nineteen experimental inputs. Cosmology adds at least six more. Together, these twenty-five numbers encode all known physics, spanning thirty orders of magnitude. The Standard Model offers no explanation for any of them. The Canvas Model reduces these twenty-five numbers to: zero free dimensionless parameters in the laws (the Machine), one dimensionful parameter (the Planck scale), one computed parameter (the overall Yukawa scale), and two cosmological boundary conditions (the age of the universe and the initial fluctuation amplitude). All other physical quantities are either derived analytically or computed numerically from the theory's equations. This paper is the complete exposition of the Canvas Model. It includes the full derivations of every result, organized by sector, with cross-references to the fourteen appendices that contain the complete mathematical proofs. 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, wave intersections, emergence