Emergent Mass and Maxwell Structure from Harmonic Closure Dynamics

This work presents a unified pre-geometric framework in which a single primordial frequency, ν₀, simultaneously generates both an emergent mass scale and the homogeneous structure of Maxwell’s equations. The model is based on harmonic synchronization dynamics of coupled oscillators defined on the three-dimensional torus (M=(S^1)^3). The minimal non-degenerate coherent configuration is shown to be the harmonic triad ((ν₀,2ν₀,3ν₀)), from which an emergent inertial mass naturally arises: [m_0 = {hν_0√14}{c^2}] without introducing additional free parameters. Electromagnetic structure emerges from a dynamical closure connection (A_μ=(ρ,-A)), whose associated field tensor geometrically reproduces the homogeneous Maxwell equations: [∇ · B = 0][∇ × E = -∂_t B] Within this framework: * mass is interpreted as the energetic cost required for coherent structures to resist destructive self-cancellation;* electromagnetism emerges as the differential geometry of synchronization coherence;* electromagnetic waves correspond to oscillatory modes of the closure connection. The paper therefore unifies: 1. emergent mass generation;2. the geometric origin of Maxwell structure;3. a pre-geometric interpretation of physical existence as persistent coherent synchronization. Several major open problems remain, including: * derivation of the inhomogeneous Maxwell equations;* full emergence of Lorentz invariance;* derivation of fermionic structure;* possible connections with Standard Model gauge groups.