The Toroidal Orbit Model: A Geometric Framework for Atomic,Molecular, and Nuclear Shell Structure

Abstract We introduce the Toroidal Orbit Model (TOM), a geometric seat-filling framework forelectronic shells in atoms and molecules and for nucleonic shells in nuclei. TOM formalizes “tubeseats” around a central potential, derives the 2n2 electron-capacity rule via seat tiling, constructsthe nuclear magic-number sequence 2, 8, 20, 28, 50, 82, 126 without tunable parameters (3L+2Frule), and proposes compact templates for molecular angular distributions (ARPES/HHG). Wepair the framework with preregistered, equal-complexity head-to-head tests in atomic, molecular,and nuclear regimes and provide a reproducibility runbook.