Geometric Nuclear Stability: From Bipartite Structure to the Island of Stability

We derive nuclear stability rules and decay predictions from the geometric principle that nuclei form bipartite structures where protons and neutrons never directly bond to same-type particles. This single constraint, arising from the rotation (proton) versus oscillation (neutron) modes of the icosahedral nucleon structure, explains: (1) N≈Z for light nuclei, (2) N>Z for heavy nuclei, (3) even-even isotope dominance, (4) why only four odd-odd nuclei are stable, (5) nuclear magic numbers, and (6) decay mode selection. All seven magic numbers (2, 8, 20, 28, 50, 82, 126) are derived from icosahedral geometry, including 82 = 2F+E+V and 126 = D!×(F+1). The free neutron half-life emerges as t½ = E×F + V + χ = 614 seconds (0.13% error). RIKEN's 2023 observation that ²⁸O is unbound confirms a crucial boundary condition: magic numbers quench at extreme N/Z ratios (>2), empirically validating where icosahedral geometry gives way to continuum effects. We predict the Island of Stability lies at Z=120=D!×F with N=184; these predictions become testable as superheavy elements are synthesized.