Cosmology of Quantum Triadic Graphs

This paper presents Cosmology of Quantum Triadic Graphs: Structural Emergence in the Relational Time Superposition Hypothesis (RTSH) Model, the first computational formulation of a cosmological network governed by quantum-inspired causal rules. In this model, new nodes attach to a growing causal graph through a Grover-based quantum selection mechanism, followed by a coherence-driven quantum triadic closure and a semilocal causal noise term. The resulting networks exhibit filamentary and quasi-spherical morphologies, high clustering coefficients, truncated power-law degree distributions, and small-world causal coherence — structural signatures reminiscent of the large-scale cosmic web. The paper interprets these properties within the RTSH framework, where spacetime emerges as a self-optimizing network of quantum collapses. To our knowledge, this is the first formulation of a quantum triadic closure mechanism — a coherence-driven analogue of classical triadic closure — designed to capture local reinforcement of causal correlations in quantum-relational networks. The full simulation code (Qiskit + NetworkX + Matplotlib) is included as Appendix C and reproduces all figures and metrics discussed in the text. Keywords:RTSH, quantum networks, causal graphs, triadic closure, Grover algorithm, emergent spacetime, complex systems, cosmology of graphs.