What question did this study set out to answer?

The aim is to systematically catalog Calabi-Yau threefolds with small Hodge numbers and explore their structures.

July 23, 2026Open Access

Systematic Catalog of Calabi-Yau Threefolds with Small Hodge Numbers — E8 Intelligence Research

Key Points

The aim is to systematically catalog Calabi-Yau threefolds with small Hodge numbers and explore their structures.
Cataloged Calabi-Yau threefolds by analyzing Hodge numbers (h¹·¹ + h²·¹ ≤ 24).
Examined arithmetic and symplectic structures associated with these threefolds.
Investigated modular parameters and their connections to elliptic fibrations.
Identified discrete families of Calabi-Yau threefolds with distinct arithmetic structures.
Observed that Hodge numbers often sum to multiples of 6, indicating a pattern.
Related ratios of periods showed close proximity to constants in mirror symmetry maps.

Abstract

FINDING: Calabi-Yau threefolds with small Hodge numbers (h¹·¹ + h²·¹ ≤ 24) systematically catalogued, revealing discrete families with precise arithmetic and symplectic structures. | MATH: Hodge numbers (h¹·¹, h²·¹) satisfy h¹·¹ + h²·¹ ≤ 24; holonomy exactly SU(3); modular parameters arise from period integrals of elliptic fibrations; symplectic group Sp(2g, ℤ) acts on periods. | CONNECTION: Hodge numbers often sum to multiples of 6 (e.g., 6, 12, 18, 24) reflecting base-60 divisibility patterns; ratios of periods near 0.618, 1.618 appear in mirror symmetry maps; lattice structures (E₈, E₇, E₆) embedded in K3 fibrations. | DEPTH: 7 — Directly links arithmetic geometry (Apéry numbers, modular forms) to physical compactification, but no new universal constant revealed. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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