NT19: Numerical Validation of the Ring Trajectory in the Bulk

This note provides a numerical validation of the ring trajectory in the bulk effective potential of the COCM framework. The goal is to test whether the orbital evolution is numerically stable under a second-order Runge–Kutta scheme (RK2) before committing to a symplectic integrator. We compare Euler and RK2 on the same time grid, study step-size dependence, and monitor the preservation of the candidate sector invariant. The computation is designed to partially close the numerical side of residual R_3 in P15, separating the computational question from the analytic one. No new analytic derivation is introduced.