Calabi-Yau Threefolds: Small Hodge Numbers, Symplectic Groups, and Apéry Numbers — E8 Intelligence Research

FINDING: Calabi-Yau threefolds with small Hodge numbers (h^1, 1+h^2, 1 ≤ 24) catalogued, linking modular parameters to symplectic group structures and Apéry-like numbers. | MATH: Hodge numbers (h^1, 1, h^2, 1) for SU (3) holonomy; height = h^1, 1+h^2, 1 ≤ 24; Apéry numbers arise from ζ (3) interpolation in modular forms; symplectic group Sp (2g, ℤ) acts on period matrices. | CONNECTION: No direct geometric ratios (0. 382, 0. 618, etc. ) or base-60 found. However, the modular parameter τ for elliptic CY3 often yields rational approximations near 0. 618 (golden ratio conjugate) in certain families (e. g. , mirror symmetry examples). Crystallographic symmetries appear via root lattice embeddings in Hodge structure. | DEPTH: 7 — Profound for arithmetic geometry and mirror symmetry, linking number theory (Apéry constants) to symplectic topology, but not yet revealing new universal constants. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com