Pulsars and Millisecond Pulsars III: Tracing Compact Object Dynamics in Globular Clusters with NBODY6++GPU

Neutron stars in globular clusters undergo complex evolutionary pathways involving binary interactions, mass transfer, and dynamical exchanges. While direct N-body simulations like NBODY6++GPU have successfully modeled stellar dynamics and compact object formation, the explicit tracking of pulsar spin evolution and magnetic field decay has historically been absent. In Papers I and II of this series, we identified this gap and proposed seven distinct evolutionary scenarios for pulsars in dense stellar environments. Here we present a comprehensive case study from an existing simulation with N=105,000 particles, demonstrating concretely where a neutron star forms and evolves for 200 Myr without pulsar physics tracking. We compare our approach with the recent implementation and detail our seven-scenario framework incorporating magnetic dipole spin-down, exponential field decay, environmental torques, accretion-driven spin-up, gravitational wave radiation, and merger dynamics. The neutron star Pulsar973 formed at t=800 Myr with an anomalous post-supernova mass of 5.35 M⊙, evolved to 2.52 M⊙ by t=1000 Myr, yet lacks all pulsar parameters: period P, period derivative P˙ , magnetic field B, and scenario classification. We provide complete mathematical formulations with literature references for each scenario, demonstrating integration points within NBODY6++GPU’s Hermite scheme, Ahmad-Cohen neighbors, KS regularization, and BSE stellar evolution. Our framework enables scenario-based evolution, complementing population synthesis approaches.