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.