Topological and Arithmetic Rigidity of the 861-Node Vorton Lattice on the Two-Torus

The stability of the 861-node toroidal vorton lattice is established by five mutually reinforcing principles that eliminate arbitrary cutoffs and prevent turbulent mode decay: Solenoidal Dipole Dynamics: Three-dimensional vorton dipoles maintain exact incompressibility off their singular cores without artificial smoothing. Reconnection events introduce singular inviscid dissipation, providing an irreversible non-Hamiltonian drain that prevents high-frequency turbulent blow-ups. Toroidal Regularization: Compactification onto a flat two-torus eliminates boundary losses and forces a zero Euler characteristic. This guarantees an unfrustrated, globally defect-free six-fold coordination while mapping infinite Biot–Savart dipole sums into an exact Weierstrass elliptic function. Heegner Arithmetic Firewall: The lattice modulus is locked to the terminal class-number-one imaginary quadratic field with discriminant negative 163. Because no unramified abelian extensions exist, continuous shear deformations are forbidden by an arithmetic energy barrier. Johnson Manifold Spectral Gap: The 861 nodes map isomorphically to the Johnson graph J(42, 2), producing an exact integer Laplacian Fiedler gap of 42 with a 41-fold degeneracy. This multiplicity mirrors Euler's maximal prime-generating constant, creating a spectral mass barrier that suppresses low-frequency wave excitations. Dedekind Casimir Tension: Partitioning the 861 nodes across a 72-fold modular gear symmetry leaves a structural defect of negative one twenty-fourth, exactly matching the modular weight of the Dedekind eta function. This generates an intrinsic topological tension that stabilizes inter-vorton spacing against both expansion and collapse.