Variety–Coherence Optimization: A Relational Principle for Emergent Spacetime

We propose a relational framework in which spacetime emerges from informational coherence rather than presupposed geometry. The central mechanism, Variety-Coherence Optimization, maximizes diversity of relational states while preserving local compatibility. This yields a suppression kernel from which coherent patches form and stabilize once a phase-dispersion threshold is reached. Saturated patches act as irreducible units whose propagation defines a directed acyclic hypergraph, providing causal order without background structure. A Fourier-series duality then maps internal phase structure into discrete spatial geometry, offering a spectral notion of locality. The framework reproduces features associated with holography and causal sets while remaining model-independent, highlighting coherence saturation as a unifying principle for emergent spacetime.