G-Loops: Paired Winding Formation, Entanglement Coupling, and Stable Composite Structures in a Bounded Phase System

This paper presents a bounded phase-field model that produces stable composite structures from paired winding defects (“G-loops”). The system evolves within a single bounded spatial cell and does not involve anything traveling through spacetime faster than light. Earlier versions used “superluminal” language that was misleading — this has been corrected here. Key behaviors observed: – formation of paired winding structures – entanglement-like coupling between pairs – a critical threshold (~5–7 entangled pairs) where the system transitions from unstable topology to a stable configuration – convergence toward eigenstructure-like behavior (overlap → ~0.999, decreasing internal variance) The result is a stable emergent composite structure formed by entangled phase defects. This is not a claim of a fundamental particle. The closest interpretation is a quasiparticle-like structure within a bounded dynamical system. The paper includes full mathematical framing, simulation method, and validation results.