The Structural Field Equation 1.3 (updated 7. April 2026)

This work derives the fundamental equations of physics from the ontological principles of Structure Theory. A structural field equation is formulated whose four parameters (structural diffusivity, relaxation timescale, transition timescale, and transformation threshold) are independently measurable and physically interpretable across domains. Three results are established with derivation: Exponential relaxation is the sub-threshold, spatially uniform limit of the structural field equation. Radioactive decay, capacitor discharge, thermal equilibration, and mechanical damping are structurally identical processes distinguished only by the physical identity of their parameters. Quantum mechanical wave dynamics is the reversible, conservative, sub-threshold limit of the structural field equation. The free Schrödinger equation follows by removing dissipation and applying a Wick rotation. The full Schrödinger equation with potential follows by treating the environment as a static structural field with a local bias rate. These derivations are exact. Irreversible threshold transitions (phase transitions, activation processes, structural failure, regime shifts) are the above-threshold limit of the same equation. Onset sharpness, hysteresis, and front propagation velocity are quantitative predictions of the framework. Physical laws are not assumed. They are derived from structural dynamics. This work is the third in a connected series. Structure Theory establishes the ontological foundation. The companion work on temporal order derives time from structural transformation. The present work derives the equations of physics from the same foundation.