Relational Field Theory (RFT)

Relational Field Theory (RFT) is a structural framework for understanding when strong effects—such as dissipation, concentration, or coherence—emerge in systems governed by aggregation dynamics. Rather than introducing new equations, RFT identifies the structural conditions under which these effects activate or fail. In particular, the framework shows that smoothing alone is not sufficient; activation requires the emergence of relational dominance and an exterior gap among competing contributions. This project develops and tests RFT through a sequence of linked papers that move from theory to computation. Project Structure The work is organized into the following components: Framework (RFT): Defines relational fields, dominance, exterior gap, coercive activation, and failure regimes Burgers Structural Theory: Establishs the dominance mechanism rigorously in a canonical nonlinear PDE Navier–Stokes Diagnostics: Defines measurable quantities for testing relational dominance in 3D turbulence Computational Framework: Provides a pseudo-spectral solver and numerical pipeline Experiment Design: Specifies reproducible procedures for extracting dominance diagnostics Goal of the Project The objective is not to solve Navier–Stokes directly, but to provide a falsifiable framework for testing whether structural dominance mechanisms play a role in turbulence. Status Framework established Structural mechanism validated in Burgers flow Diagnostics and computational tools defined Numerical testing in 3D flow in progress