Light-Nuclear Structure as Polytope Closure on a Hexagonal Boundary

This manuscript reports a correspondence between light-nuclear structure and the closure conditions on regular triangular polytopes. Within the framework’s existing architecture, a nucleon is a Z₃ triad — a three-fold closure across the boundary lattice’s three axes, established in the companion manuscript on confinement. Read as a polytope vertex set, assemblies of such triads admit closure only under specific counting conditions. Those conditions reproduce the observed pattern of light-nuclear stability: the mass-number gaps at A=5 and A=8, the composition of the stable light nuclei, the alpha-cluster structure of A=12, 16 and 20, and the alpha counts of the doubly magic N=Z nuclei. All results follow from counting; no reaction rates, cross-sections, or binding energies are computed or required. The correspondence is reported as a structural result. Formation rates are outside its scope, and the manuscript is explicit about what it does not derive.The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). The author directed this process, evaluated and selected among proposed derivations, and takes full responsibility for the accuracy and originality of the final work.