We introduce a dissipative dynamical framework in which prime numbers arise as asymptotic attractors of a coupled curl–SO (3) evolution. Each prime is represented as a unit axis on S2S²S2, while composite integers correspond to transient states generated by the noncommutative accumulation of rotations induced by prior primes. The system evolves according to a curl-driven equation with axial damping and phase-mismatch feedback, coupled to a phase-locking dynamics that drives all active branches toward a π/2/2π/2-lattice. We define an energy functional combining horizontal curl residuals and phase mismatches, and prove that it decays exponentially under the dynamics. As a consequence, all transverse rotational components vanish, phase mismatches converge to π/2/2π/2-locking, and a new stable axis emerges as the normalized limit of the flow. This establishes primes as energy-zero fixed points of a dissipative noncommutative curl–rotation system. The framework unifies scalar mod-4 closure, complex residual cancellation, and SO (3) torus flip mechanisms within a single PDE-driven model, providing a dynamical interpretation of prime emergence and suggesting connections to spectral theory and gauge-theoretic flows.
Jeong Min Yeon (Thu,) studied this question.