The Planck Sheet Model: A Geometric Theory of Elementary Particles on a Discrete 5D Sheet

Abstract

We propose a geometric model of fundamental physics in which space is represented as a discrete 5-dimensional sheet with an elementary cell of Planck size. Our 3D Universe is an embedded brane in this sheet. Particles are interpreted as topological defects (nodes) of the sheet. The key claim: particle masses are emergent from the geometry of projection of a higher dimension onto a fractal brane. From a single cosmological parameter — the baryon asymmetry — and purely geometric constants, the model derives masses of leptons and quarks, the fine-structure constant, and the anomalous magnetic moment. This deposit includes the main preprint (LaTeX sources), three mathematical supplements (Koide formula, magnetism, standing waves), simulation code, and numerical results. This is a heuristic speculative model. Numerical agreement with observed values is presented as phenomenolog ical motivation. Disclaimer: In preparing the mathematical formalization of this work, tools based on Large Language Models (LLM) were used to translate geometric concepts into formal mathematical language. All fundamental ideas, postulates, and derivations belong to the auth or.