The Harmonic Triad Theory: A Pre-Geometric Framework Based on Synchronization Dynamics V2

This work proposes a pre-geometric theoretical framework in which spacetime, particles, and gauge-like structures emerge from synchronization dynamics and closure relations in networks of coupled phase oscillators. The framework introduces the harmonic triad as the minimal non-degenerate coherent structure and explores possible connections with emergent geometry, topological defects, and collective excitation modes.