Relational Self-Coherence Framework: A Unified Instability Functional for the Emergence of Geometry and Quantum Behaviour

This work presents the complete mathematical and conceptual formulation of the Relational Self-Coherence Framework — a unified physical model in which relationships, rather than spacetime or fields, are taken as the fundamental building blocks of reality. In this framework, all physical laws emerge from the minimisation of a single global quantity: the Total Relational Instability Functional, \mathcal{I} = \sum_{i,j} f(\mathbf{H}_{ij}, \Delta \ell_{ij}, \Delta \sigma_{ij}, S_{ij}, W_{ij}), The model proposes a probability rule for the actualisation of relations, P(R_{ij}=1) \propto \left(-\frac{\delta \mathcal{I}}{\delta R_{ij}}\right)\exp(-S_{ij}), Through coarse-graining and variation of the instability functional, the framework naturally reproduces: Einstein-like geometric structure, quantum path-sum amplitudes, conservation laws, interference and phase behaviour, and emergent constants such as , , and . This release includes the full extended formulation, derivations, tensor definitions, and appendices, providing a complete resource for theoretical exploration, simulation, or further development.It is intended as a stable, citable reference for the emerging relational approach to fundamental physics.