Geometric Origin of CP Conservation in Strong Interactions: Solution of the Strong CP Problem in the 26 Vertex Cubic Lattice of Discrete Geometric Physics

The Strong CP Problem is one of the deepest mysteries of the Standard Model. Quantum Chromodynamics (QCD) admits a CP‑violating term parametrized by the angle θ, but experiments on the neutron electric dipole moment set the stringent limit ∣θˉ∣≲10−10∣θˉ∣≲10−10, which is 10 orders of magnitude smaller than the natural value ∼1. Existing solutions (axion, massless quark, irreversible symmetries) either introduce new particles or rely on fine‑tuning not derivable from first principles. In Discrete Geometric Physics (DGP), space is a 26‑vertex cubic lattice with the topological invariant Σw = 14. All gauge fields arise from the displacement field on the lattice edges. In this work, we prove that the θ‑term is identically zero due to the lattice geometry and the weight relation wG=2wE=4wVwG=2wE=4wV. The cancellation is topological and does not depend on the particular field configuration. Quantum corrections (Planckian jitter) are exponentially suppressed: δθˉ≈4.6⋅10−17δθˉ≈4.6⋅10−17, far below the experimental limit. CP violation exists only in the electroweak sector, where it is derived from geometry and agrees with experiment (δCP=68.7∘δCP=68.7∘). The axion is not required and is predicted to be absent. All results are obtained from geometric invariants (Σw = 14, θ = arcsin(1/√3), φ = (1+√5)/2) and numerical solution of minimization equations on the lattice. No fitting parameters are introduced. The theory provides testable predictions, including an extremely small neutron EDM (dn≈4.6⋅10−33 e⋅cmdn≈4.6⋅10−33e⋅cm) and null results from axion searches.