RZS Series: The Relational Zero State Hypothesis: Spectral Graph Dynamics and the Emergence of Spacetime Geometry

We propose the Relational Zero State (RZS) hypothesis as a pre-geometric framework in which spacetime emerges from purely relational dynamics. The RZS is defined as an unstable state of maximal relational potentiality, devoid of metric, time, or causal structure. Geometry arises through the dynamical evolution of relational graphs governed by spectral flow of the graph Laplacian. In the dense-connectivity limit, spectral convergence leads to an effective hydrodynamic regime and the emergence of a continuum spacetime geometry with Lorentzian structure. The framework naturally predicts Pareto-type distributions of relational clustering, providing a potential observational signature at cosmological scales. The RZS is presented as an open conceptual and mathematical research program, complementary to existing approaches to emergent spacetime and quantum gravity.