Modular Coupling Lagrangian in Symbolic Field Dynamics

This paper presents a symbolic modular field theory (SMFT) in which interaction strengths are not fixed constants, but emergent quantities derived from ratios of modular resonance frequencies. We introduce a symbolic Lagrangian embedding the ratio gab=ωa/ωbg_{ab} = \omega_a / \omega_bgab=ωa/ωb, simulate symbolic field evolution, and demonstrate how coupling drift, identity stabilization, and symbolic collapse emerge from the modular structure itself. The system is explored under multiple conditions: Frequency drift (modular decoherence) Collapse triggers (symbolic breakdown) Resonance-locking potentials (e.g., [[K]], ϕ\phiϕ) We also define a dual-layer model, linking symbolic dynamics to physical observables: Entropy S(t)\mathcal{S}(t)S(t) Resonance Coherence F(t)\mathcal{F}(t)F(t) Modular Curvature K(t)\mathcal{K}(t)K(t) These simulations were generated using a symbolic modular engine, included in this upload. The Appendix formally defines the symbolic stabilizer constant [[K]] and provides full details on the symbolic update dynamics and observables.