UNIFICATION III - Toward a Dynamical Formulation of the Lightlike Boundary Framework

This work is the third technical paper in the UNIFICATION series and represents the first major step from structural interpretation toward a possible dynamical formulation of the Chi Framework.In the earlier papers, the framework introduced the shared lightlike boundary between relativistic and quantum descriptions, together with the boundary parameter χ, the deviation parameter δ, and the phase ratio χϕ. The present paper extends those ideas by exploring how the framework might be expressed in field-like, wave-like, and variational forms.A central contribution of this work is the introduction of the possibility that χ may be treated as a spacetime-dependent field, χ(xμ), allowing the framework to evolve across space and time rather than remaining purely algebraic. This leads to the exploration of candidate governing equations involving wave propagation, phase evolution, and nonlinear self-limiting behavior.The paper examines several possible mathematical directions, including minimal field structures, wave-like propagation equations, variational and action-based formulations, and nonlinear equations that may constrain systems near the shared lightlike boundary.The work also explores possible geometric interpretations in which variations in χ or δ may correspond to curvature-like behavior, and considers whether the framework may eventually connect relativistic, quantum, and geometric descriptions through a shared evolving phase structure.In addition, the paper discusses possible future observational or experimental implications and outlines directions for further development, including cosmological interpretation and hidden structural limits involving zero-like and infinity-like behavior.The present work remains exploratory. No final governing equation is claimed, no modification to established relativity or quantum theory is proposed, and no empirical claims beyond known physics are made. The contribution of this paper is to identify plausible mathematical pathways by which the Chi Framework may evolve from an interpretive structure into a predictive or dynamical theory.This paper serves as a bridge between the structural interpretation papers and later works that develop stronger candidate governing equations and deeper formal synthesis. Currently Available: UNIFICATION 0 - A Shared Lightlike Boundary for Relativity and Quantum Theory - v1.00 https://doi.org/10.5281/zenodo.19860494 UNIFICATION I - Phase Structure and the Lightlike Boundary - v1.00 https://doi.org/10.5281/zenodo.19862660 UNIFICATION II - Implications of the Lightlike Boundary and Phase Structure - v1.00 https://doi.org/10.5281/zenodo.19863301 UNIFICATION III - Toward a Dynamical Formulation of the Lightlike Boundary Framework - v1.00 https://doi.org/10.5281/zenodo.19895578 UNIFICATION IV - Consequences and Implications of the Chi Framework v1.00 https://doi.org/10.5281/zenodo.19896296 UNIFICATION - The Chi Framework - Eight Lessons on the Boundary Between Relativity and Quantum Mechanics - v1.00 https://doi.org/10.5281/zenodo.19863601 Soon to come will be: UNIFICATION V - Chi Framework and, Concerning the Absence of a Governing Equation - v1.00 and... UNIFICATION VI - From Limit Structure to Rotational Interpretation - v1.00