A Graph-Theoretic Model with Three Primitives: Structural Consequences and Physical Correspondences

A graph-theoretic model is presented with one type of object (a node), two boundary conditions on connectivity, and a substitution principle. Structural consequences are derived without additional assumptions, including composite objects defined by density gradients, a uniqueness constraint preventing duplicate subgraphs, and a formal occupancy bound limiting coexistence of similar subgraphs at a single location. Self-referential fixed-point structures arise as natural topological features of the graph, and the D1-D4 conditions developed in three companion papers on the Riemann Hypothesis are shown to be graph-topological properties of these structures. Physical correspondences are identified: the uniqueness constraint reproduces quantum exclusion; shared-node subgraphs reproduce entanglement without nonlocality; the critical interface threshold reproduces event horizons and black hole information-theoretic properties. The tension between general relativity and quantum mechanics is identified as an instance of irreducible complementarity - two readings of the graph at different scales that coexist without requiring reduction of either to the other. This is the fourth paper in a series. Companion papers: "The Riemann Hypothesis as a Fixed-Point Phenomenon" (doi:10.5281/zenodo.19425929), "Below the Threshold: Curvature Invariants of the Prime-Zero Dependency Cycle" (doi:10.5281/zenodo.19426045), and "The Research Landscape Around the Riemann Hypothesis in Light of the Structural Classification" (doi:10.5281/zenodo.19426099).