Heegner Points, Fricke Involution Crossing Duality, and O(1) Topological Relaxation in Solenoidal Vorton Manifolds

This work establishes an exact mathematical equivalence between the arithmetic classification of Fricke modular involution fixed points on modular curves and the Hamiltonian fluid mechanics of three-dimensional solenoidal vortex reconnections. While classical digital computers require polynomial-logarithmic runtime scaling to classify these complex multiplication isogenies through combinatorial search, a continuous fluid medium resolves the underlying Diophantine constraints autonomously through topological relaxation. In this framework, the Fricke modular involution represents the physical exchange between the longitudinal advection channel and the transverse shear channel during vortex filament cutting and reconnection. The modular fixed points correspond to kinematic stagnation points of the fluid rate-of-strain tensor, where convective phase slip vanishes, strain alignment becomes planar, and incoming and outgoing acoustic impedances match symmetrically. When embedded on a discrete spectral manifold anchored to the maximal one-class imaginary quadratic field and a regular Johnson association scheme, anomalous enstrophy dissipation drives the fluid along a Lyapunov free-energy gradient directly into the self-dual modular attractor. Because the exponential convergence rate is bounded from below by an invariant discrete spectral gap that does not scale with the modular level, the physical substrate converges to the exact arithmetic solution in constant physical relaxation time, circumventing classical digital complexity limits through topological admissibility.