Prime-Lattice Dynamics and Nuclear Isotopy: A Universal Model Framework Analysis of Elemental Stability Boundaries

This comprehensive analysis demonstrates that nuclear isotopic stability patterns—including the empirical boundaries of 81 stable chemical elements, the universal ceiling of 10 stable isotopes per element, and the instability of technetium (Z=43) and promethium (Z=61)—arise deterministically from arithmetic constraints in a prime-indexed fractal information lattice. Within the Universal Model Framework (UMF), these features are shown to follow from 6n ± 1 prime geometry and Pascal–Sierpiński duality, eliminating the need for ad hoc parameters in conventional nuclear shell models. The paper derives the unique 20-element Reinisotope set, reproduces Plichta’s 4:19 neutron-rich distribution pattern, and offers comprehensive visualizations and comparative analysis. These results suggest nuclear physics is a manifestation of deeper arithmetic order, with isotopic multiplicity boundaries emerging inevitably from recursive prime structure rather than statistical quantum mechanics This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.