INTERNATIONAL JOURNAL OF PROFESSIONAL STUDIES

This paper develops a closed theorem system for high-dimensional Calabi–Yau saturation in the precise toric, hypersurface, stringy, and statistical ensembles defined in the text. The construction proves the existence of compact Calabi–Yau n-folds in every dimension, exact adjunction and Chern-class formulae for the degree-(n + 2) hypersurface tower, explicit Hodge-number derivations from the Jacobian ring, entropy lower bounds for reflexive-polytope families, quantitative phase-function asymptotics, Berry–Esseen convergence for the Poisson Hodge model, Lindeberg log-normal saturation, Hagedorn equivalence, and Batyrev mirror invariance for stringy Hodge laws. The resulting closure theorem shows that every conclusion used by the paper follows from stated definitions, classical theorems, or verified ensemble hypotheses, without hidden classification assumptions.

Keywords: Calabi–Yau manifolds; reflexive polytopes; mirror symmetry