Nuclear Magic Numbers from Wave Geometry: A Zero-Parameter Derivation from Z₃ Möbius Topology

The nuclear magic numbers — 2, 8, 20, 28, 50, 82, and 126 — mark nucleon counts of exceptional nuclear stability. Since 1949 they have been explained by the nuclear shell model, which requires adding a spin-orbit coupling term with fitted constants to a harmonic oscillator potential. The sign and strength of that coupling are chosen to reproduce the known magic numbers, not derived from a deeper principle. This paper presents a geometric derivation that reproduces all seven magic numbers with zero free parameters. The single input is a biconical horn with Z₃ Möbius topology — the resonant cavity formed by a standing wave on a one-third-twist strip in Dimensional Oscillation Theory. The 30° cone angle is…