The Canvas Model: A Complete Derivation of the Standard Model from a Theory of Tethers

This paper presents a complete derivation of the Standard Model of particle physics from a theory of fundamental constraints called tethers. A tether is a constraint that binds continuous degrees of freedom into discrete actualities. Four tether types—spatial, parameter, symmetry, and intersection—are specified by eight primitive tether parameters (Order, Amplitude, Acceleration, Polarity, Chirality, Dimension, Angle, Charge) and governed by four tether interaction rules: the Unified Wave Equation, the Threshold Condition, the Eigenvalue Equation, and the Feed Equation. The framework distinguishes between the Machine—the timeless tether laws with zero free dimensionless parameters—and the State—the contingent configuration of our universe specified by two boundary conditions. Every Standard Model parameter emerges as an eigenvalue of a specific tether constraint on a specific geometric subspace. What this paper derives: The three gauge couplings are derived in closed form from the stability bounds and dimensional reduction of the charge tethers: g_1^2 = 25\pi^3/2048, g_2^2 = 25\pi^3/3072, g_3^2 = 25\pi^2/1024, with ratios 1 : 2/3 : 2/\pi. The CKM and PMNS mixing matrices emerge from the symmetry tethers of the Higgs directions in the internal 3D space, with \theta_{13} = \arcsin(1/(3\sqrt{5})) \approx 8.57^\circ matching the observed central value exactly. The fermion mass hierarchy is produced by the Polarity Domain transition—an intersection tether amplified by the gauge-vev coupling—with all five quark mass ratios derived at the Planck scale within a factor of 1.6 of observation. The neutrino masses follow from sequential tether crossing and the seesaw mechanism, with the atmospheric splitting |\Delta m_{32}^2| = 2.60 \times 10^{-3} eV^2 within 6% of observation and a prediction of normal mass ordering. The CP-violating asymmetry parameter \alpha = (\pi-2)/(\pi+2) \approx 0.222 emerges from the ratio of Acceleration to Polarity tether weights. The CKM phase \delta_{\text{CKM}} \approx 69^\circ and the baryon asymmetry \eta \approx 4.9 \times 10^{-10} follow from the primitive composition of the fundamental fields. The cosmological constant, electroweak scale, and dark matter nature follow from the State boundary conditions. The Machine has zero free dimensionless parameters. All Standard Model parameters are eigenvalues of the tether constraints. 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 Machine, one dimensionful parameter (the Planck scale), one computed parameter (the overall Yukawa scale, with natural scale \sim 1), and two cosmological boundary conditions (the age of the universe and the initial fluctuation amplitude). All other physical quantities are either derived analytically or specified for computational refinement. Keywords: tethers, canvas model, gauge coupling unification, fermion masses, CKM matrix, PMNS matrix, neutrino masses, CP violation, baryon asymmetry, dark matter, Standard Model, emergence