Lattice Geometry and Fundamental Constants

This framework derives fundamental physical constants and cosmological dynamics directly from the discrete geometry of an eight-hundred-sixty-one-node simplicial torus anchored at a maximal Heegner discriminant: Fine-Structure Constant: The low-energy electromagnetic coupling emerges as an exact infrared fixed point defined by the geometric aspect ratio of the discrete lattice. Dynamic Dark Energy: Cosmic expansion stretches the interacting vorton network to produce a running vacuum energy density that scales with the expansion rate, naturally yielding an evolving equation of state consistent with modern cosmological surveys. Particle Constants: The proton-to-electron mass ratio is established by the invariant phase-space volume ratio of a five-dimensional topological embedding relative to a one-dimensional loop, while the electroweak mixing angle is fixed by the discrete subgroup symmetry hierarchy of the manifold. Field-Free Cosmic Inflation: Rapid cosmic expansion is driven by a deterministic, finite-time enstrophy runaway caused by localized vorton collapse and lattice commensurability defects, eliminating the need for an ad-hoc inflaton scalar field.