Foundation — The Canvas Model: How Wave Intersections on a Pre-Geometric Surface Generate Gauge Couplings, Particle Content, and the Dark Energy Density

We present a framework in which all physical phenomena emerge from waves intersecting on a pre-geometric two-dimensional surface called the canvas. The framework is specified by eleven postulates. From these postulates, with zero adjustable dimensionless parameters in the Machine sector, we derive three results that no other theory has produced from first principles. First, the gauge couplings at the Planck scale. The strong coupling is \alpha_s(M_P) = 25\pi/4096 \approx 0.019175. The value required to reproduce the measured low-energy coupling under Standard Model running is \alpha_s(M_P)_{\text{required}} \approx 0.019054. Agreement: 0.63\%. The three couplings satisfy g_1^2 : g_2^2 : g_3^2 = 1 : 2/3 : 2/\pi. No fitting. No free parameters. The ratios emerge from the projection of higher-dimensional gauge fields onto the 2D canvas. Second, the complete particle content of the Standard Model. The crossing taxonomy yields exactly three fermion generations from the three observable combinations of dynamic primitives. Combined with the property primitives, this produces the full particle set: 37 observed particles plus 3 predicted right-handed neutrinos. The framework forbids fourth-generation fermions, SU(4) gauge bosons, spin-3/2 particles, and right-handed SU(2) couplings. Third, the dark energy density. Baseline subtraction proves that uniform vacuum energy does not gravitate, resolving the old cosmological constant problem. The residual dark energy comes from the geometric ratio of space to time field subspaces, yielding \Omega_\Lambda = 3/(3+\sqrt{2}) \approx 0.6796, in agreement with the observed 0.685 \pm 0.007 to within 0.7\%. Additional derived results include the CKM Wolfenstein parameter \lambda = 1/5, the CKM hierarchy, PMNS \theta_{23} = \pi/4 and \theta_{12} \approx 33.7^\circ (leading order), Majorana phases, the resolution of the strong CP problem (\theta_{\text{QCD}} = 0), the asymmetry parameter \alpha = (\pi-2)/(\pi+2) \approx 0.222 emerging from two independent geometric routes, and a unified mechanism for inflation and dark energy as environmentally-dependent voxel nucleation. The framework makes a falsifiable prediction: the local Hubble expansion rate should correlate with environmental density, being maximal in cosmic voids and suppressed in bound systems. This differs from \LambdaCDM where dark energy is uniform. Upcoming surveys can test this. Open problems — the full fermion mass spectrum, the seesaw scale, the CKM phase, and quantitative inflationary predictions — are explicitly identified with the constraints that any solution must satisfy. The fact that a small set of postulates about wave dynamics on a 2D surface produces specific, parameter-free numbers matching observation — numbers that were not put in by hand but emerged from geometry — suggests the Canvas Model captures genuine features of nature's underlying structure. Keywords: canvas model, gauge coupling unification, particle content, dark energy, cosmological constant, CKM matrix, PMNS matrix, strong CP problem, inflation, emergence, wave intersections, pre-geometric surface, falsifiable predictions