Gauge and Quantum Dynamics from the GEF/GEP Network: Topological origin of fermions and emergent spacetime dynamics

This paper proposes a network-based model of spacetime in which geometry, gauge interactions, and fermionic matter emerge from the topology of a microscopic Planck-scale network. The framework combines the Geometric Entropy Field (GEF) and the Geometric Entropy Principle (GEP) to describe spacetime as a dynamic graph of Planck-scale cells connected by microscopic wormhole links.

In this picture, gravitational dynamics arise from variations in the density of network connections, gauge fields correspond to oriented phase flows along network links, and fermions appear as topological excitations in the form of twisted Möbius-type loops. A topological argument based on the fundamental group π1(SO(3))=Z2\pi_1(SO(3)) = \mathbb{Z}_2π1(SO(3))=Z2 shows that such twisted loops exhibit spinorial transformation properties and therefore correspond to spin-½ particles.

Stability analysis using the Călugăreanu–White–Fuller theorem suggests that only three low-energy twisted loop configurations are stable, providing a possible topological explanation for the three observed fermion generations. In the continuum limit the model reproduces the Newtonian gravitational equation, Maxwell gauge fields, and the Dirac equation for fermionic excitations.

The framework offers a unified topological interpretation of spacetime geometry, gauge interactions, and matter as emergent phenomena arising from a single microscopic network structure.