Resolution of the Gravitational Singularity through Discrete Gear Geometry Cutoffs at the Planck Scale

The gravitational singularity presents one of the most critical mathematical breakdowns in General Relativity, occurring at the center of black holes and the initial state of the Big Bang when the radius approaches zero, leading to infinite gravity. Unifying gravity with quantum mechanics has been stymied by this infinity. In this paper, we utilize the H3QM (Holographic Hologram-Holographic Quantum Mechanics) theory, which posits that space is a discrete network of physical microscopic gears, rather than an infinitely divisible continuum. This geometry establishes an absolute minimum physical length scale—the Planck length (ℓPℓP). By applying a discrete geometric cutoff to the standard gravitational equations, we demonstrate that gravity does not tend to infinity but reaches a safe, finite maximum limit. This intuitive mathematical modification permanently resolves the singularity paradox without requiring higher-dimensional paradigms like String Theory. 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.