The Nuclear Construction: Method Disclosure for Polytope Closure on a Hexagonal Boundary
Abstract
A companion manuscript reported a correspondence between light-nuclear structure and closure conditions on regular triangular polytopes, stating the results without disclosing the derivation. This manuscript supplies the method. We give the operation converting a subdivided triad into a tetrahedron, and show it is edge identification rather than any spatial folding — a distinction that blocked the construction entirely until it was corrected. We derive the parity condition determining which subdivisions can close, and show that of the eight convex deltahedra only two have a face count that is a perfect square, giving exactly the two doubly magic nuclei A=4 and A=16. We derive the mass-number gaps at A=5 and A=8 by three independent routes each, and identify both as the first four-dimensional member of their respective polytope families. We give the regularity criterion, correcting an earlier and narrower triangularity criterion that does not survive inspection. We supply the composition rule — balancing nucleon count across a two-by-two grid of type against spin on both marginals — together with the three routes that failed before it, and report an out-of-sample test that the rule passes without having been aimed at it. Every result is counting. No reaction rate, cross-section, or binding energy is computed or required, and Section X states precisely which quantities are therefore unavailable.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.
