From Nuclear–Electronic Relations to Persistent Atomic Closure: An SFM 2.0 and RCG Analysis of Quantum Binding, Atomic Identity, Excitation, Ionisation, Recombination, and Recovery

Paper 4 of 8 in the Recursive Continuity Geometry Across Physical Scale series. This paper applies the Structural Fingerprint Method Version 2.0 and Recursive Continuity Geometry to the transition from a persistent nucleus and electrons to persistent atomic closure. Established atomic physics remains authoritative for quantum binding, spectra, transition rates, ionisation thresholds, recombination, scattering and environmental interaction. The PATON framework provides a shared structural account of recurrence, persistence locking, admissibility, disturbance, interruption, recovery, ordered traversal and cross-scale handover. The paper distinguishes elemental, isotope, charge-state and electronic-state identity. Hydrogen ground, 2p, 2s and ionised configurations demonstrate how excitation may release a state lock while atomic identity persists, how ionisation interrupts neutral closure while preserving elemental identity, and how recombination may restore atomic closure through a new admissible traversal.