The Strong CP Problem: Why \theta_{\text{QCD}} = 0 in the Canvas Model

The strong CP problem asks why the QCD \theta parameter, which would produce a neutron electric dipole moment, is consistent with zero to extraordinary precision (|\theta| < 10^{-10}). In the Standard Model, \theta is a free parameter with no explanation for its smallness. Proposed solutions include the Peccei-Quinn mechanism (predicting an axion) and spontaneous CP violation. The canvas model provides a simpler resolution: \theta = 0 exactly as a consequence of the cosmic horizon. The model's spacetime is a finite 4-ball bounded by the physical horizon. On this topology, the topological charge Q = (g_s^2/32\pi^2) \int G\tilde{G} vanishes identically for all physically admissible gauge field configurations. The \theta term contributes nothing to the path integral, and \theta is not a physical parameter. The complete proof has four steps: 1. Spacetime topology: The emergent spacetime of the canvas model is a 4-ball B^4 with boundary S^3 (the cosmic horizon). This follows from the finite age of the universe and the causal structure of de Sitter space.2. Horizon boundary conditions: The gauge fields at the horizon are in the vacuum sector with winding number zero. This follows from finiteness, zero energy flux, and the fact that higher winding number configurations would require energy at the horizon.3. Extension to the interior: Any gauge field on S^3 with zero winding number extends to a field on B^4 with topological charge Q = 0. The extension is guaranteed by the homotopy extension property.4. Vanishing of the \theta term: Since Q = 0 for all physical configurations, the \theta term integrates to zero. The partition function and all correlation functions are \theta-independent. The parameter \theta is unphysical and can be set to zero. Why this differs from standard lattice QCD: Standard lattice QCD uses periodic boundary conditions on a 4-torus T^4, which has non-trivial topology and allows Q \neq 0. The canvas model's spacetime is a 4-ball with a physical boundary—the cosmic horizon. The topology is different because the universe is finite and bounded. The torus is a mathematical convenience; the ball is physical. Predictions: · No axion: The canvas model predicts that axion searches (ADMX, CASPEr, MADMAX) will return null results. Any positive axion detection would falsify this resolution.· Zero neutron EDM from \theta: The neutron electric dipole moment receives no contribution from \theta. The CKM phase contributes at the level d_n \sim 10^{-32} e·cm, far below current sensitivity.· Lattice QCD on a ball: Simulations with physical boundary conditions (a 4-ball with vacuum at the boundary) should find Q = 0 for all configurations, with no instanton effects. Keywords: strong CP problem, \theta parameter, canvas model, cosmic horizon, topological charge, 4-ball, axion, neutron electric dipole moment, lattice QCD, quantum chromodynamics