From Hadronic Units to Persistent Nuclear Closure: An SFM 2.0 and RCG Analysis of Nuclear Binding, Isotopic Stability, Decay, Reconfiguration, and Emergent Nuclear Identity

Paper 3 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 protons and neutrons to persistent nuclear closure. Established nuclear physics remains authoritative for nuclear interactions, spectra, binding energies, separation energies, decay pathways and reaction dynamics. The PATON framework provides a shared structural map of recurrence, persistence locking, admissibility, disturbance, reconfiguration, ordered traversal and cross-scale handover. The paper distinguishes nuclear formation, energetic binding, recoverable identity, persistence over a declared timescale and usability at the atomic scale. Deuterium, tritium, helium-4 and beryllium-8 are used to demonstrate the difference between bound, conditionally persistent and resonant nuclear states.