A Unified Theory of Physical Existence: From Relational Matrix to Minimal Phase Closure Triangles

This paper proposes a two-level foundation for physics: the top level is the relational matrix Rij, describing the universe’s abstract network of relations; thebottom level is the Minimal Phase Closure Triangle (MPCT), serving as thephysical implementation unit of the relational matrix. The relational matrix determines global structures and symmetries, while MPCT provides local geometricrealization and observability. We demonstrate that eigenmodes of the relationalmatrix naturally map to stable configurations of MPCTs, from which fundamentalparticles, quantization, interactions, and spacetime structures emerge. This theory combines mathematical elegance (relational matrix algebra) with physicaltestability (MPCT data detection), offering a unified framework for understanding existence from quantum scales to the cosmic whole.Keywords: Relational matrix; MPCT; Hierarchical emergence; Fundamentalunit of existence; Phase-space geometry; Relational networks; Testable foundation.