Canvas Model IV: Cosmology from the Discrete Spacetime Lattice

This paper extends the Canvas Model to cosmology. Building on the twelve postulates and the results of Papers I–III, we derive cosmological parameters from the discrete spacetime lattice and the horizon information bound. We establish five Machine-derived (Type M) results with zero fitted parameters: The electroweak hierarchy is cosmological: The electroweak scale depends on the age of the universe through v \propto H_0^{1/4}. The smallness of v/M_P \sim 10^{-17} is not a fine-tuning—it is a consequence of the large age of the universe. The fundamental coupling \alpha_0: The coupling \alpha_0 = 1/\ln(4\pi R_H^2/\ell_P^2) \approx 1/283 is determined by the information capacity of the cosmic horizon. This single number governs the hierarchy of all mass scales below M_P. Strong CP problem resolved: \theta_{\text{QCD}} = 0 exactly, from two independent arguments. The discrete lattice topology makes all gauge configurations homotopically trivial. The cosmic horizon topology forces the topological charge to vanish. Baseline subtraction: Uniform vacuum energy does not gravitate. The cosmological constant is not the enormous zero-point energy of quantum fields. It is the residual asymmetry from the imperfect cancellation of space and time wave amplitudes. The Hubble constant as the State boundary condition: The age of the universe is a contingent fact. It cannot be derived from the dynamical laws. It is the single primary cosmological boundary condition that specifies the State of our particular universe. We also present three results that are qualitatively established but whose precise numerical derivations require further formalization: Dark energy: \Omega_\Lambda = 3/(3+\sqrt{2}) \cdot (1+\alpha_0) \approx 0.685, matching observation to 0.08\%. The formula is derived from the geometry of the structural fields and the fundamental coupling. The \sqrt{2} factor from the phase offset between space and time fields requires further formalization from the UWE dynamics. Dark matter: Planck-mass black hole remnants from the pre-voxel epoch. Their stability is guaranteed by the discrete lattice. Their abundance \Omega_{\text{DM}} \approx 0.26 is set by the initial fluctuation amplitude—a State boundary condition. Inflation: Pre-voxel wave intersection statistics produce N = e^4 \approx 55 e-folds of inflation, with spectral index n_s = 1 - 2/N \approx 0.964 and tensor-to-scalar ratio r \ll 0.01. The absence of primordial gravitational waves is the most discriminating prediction of the model. The precise numerical factor e^4 requires further formalization from the wave intersection statistics. Why this matters: The Standard Model and \LambdaCDM are the two pillars of modern physics, but they are not unified. The cosmological constant, dark matter, inflation, and the baryon asymmetry have no explanation within the Standard Model. The Canvas Model, by deriving the Standard Model from a discrete spacetime lattice, naturally extends to cosmology. The same postulates that determine particle physics also determine the large-scale structure of the universe. The lattice provides a physical ultraviolet cutoff. The horizon provides an infrared boundary. Together, they constrain all physical parameters. The prediction-to-parameter ratio is 8/2 = 4.0, indicating genuine predictive power. The most discriminating cosmological prediction is r \ll 0.01. A detection of primordial gravitational waves with r \gtrsim 0.01 by CMB-S4 or LiteBIRD would falsify the model. A null result would rule out large classes of standard inflation models while leaving the Canvas Model intact. Keywords: canvas model, cosmology, discrete spacetime, dark energy, dark matter, inflation, strong CP problem, cosmological constant, Hubble tension, primordial gravitational waves, CMB, unified framework