Dark Energy as the Topological Void in 3D Kissing Sphere Packing

The Cosmological Constant Problem, often referred to as the worst theoretical prediction in the history of physics, highlights a catastrophic 10¹20 magnitude discrepancy between the quantum mechanical prediction of vacuum energy and the observed density of dark energy. In this paper, we resolve this discrepancy by applying the Holographic Hologram-Holographic Quantum Mechanics (H3QM) framework, which models the vacuum as a discrete, rigidly packed three-dimensional network of physical spherical gears at the Planck scale. We demonstrate that even in the most tightly packed configuration (face-centered cubic), rigid spheres cannot completely fill a 3D space, leaving an inherent topological void of approximately 26%. We propose that this geometric void, which cannot be occupied by mass-energy topological structures (matter), manifests macroscopically as a repulsive spatial tension. The ratio of this unoccupied geometric volume aligns remarkably with astronomical observations of dark energy density, offering a pure geometric and parameter-free explanation for the accelerated expansion of the universe. Note: This deposit includes the full paper in English (en-US), Traditional Chinese (zh-TW), and Simplified Chinese (zh-CN).