The fine-structure constant (α≈1/137.036α≈1/137.036) has remained one of the most profound enigmas in modern physics, typically requiring empirical measurement rather than pure mathematical derivation. In this paper, we introduce a novel theoretical framework based on Holographic Hologram-Holographic Quantum Mechanics (H3QM), proposing that the vacuum space is structured as a discrete, three-dimensional physical gear network. By modeling elementary particles as topological windings within this gear grid, we demonstrate that the fundamental strength of electromagnetic interaction can be derived purely from geometry. Using the topological winding number and the kissing number in 3D maximum contact stacking, we formulate the mathematical limit equation α−1≈4π3+π2+πα−1≈4π3+π2+π, yielding 137.036303...137.036303.... This analytically derived value exhibits a remarkable agreement with the highest precision experimental measurements, providing compelling evidence that fundamental constants of nature emerge naturally from the deterministic geometric properties of a discrete 3D space. Note: The full text of this paper is available in multiple languages. You can download the English (EN), Traditional Chinese (zh-TW), and Simplified Chinese (zh-CN) PDF versions from the files section below.
Cosmo Chou (Wed,) studied this question.