Unified Relational Dynamics: A Variational Framework for Emergent Geometry, Probability, and Physical Law

This document presents a fully explicit, simulation-ready formulation of a Unified Relational Dynamics Framework in which physical structure, geometry, and physical constants emerge from the minimization of a global instability functional. The work consolidates: the explicit instability kernel , the complete variational derivative , the Actualisation Rule defining relational probabilities, the metric-reconstruction algorithm allowing smooth recovery, and scaling relations for emergent constants . The document includes appendices with derivations, algorithms, and simulation protocols, providing a reproducible and falsifiable foundation suitable for independent computational and mathematical verification. This release contains a publication-ready PDF prepared for open scientific review.