Quantum Dynamics on Prime-Indexed Distinction Graphs: A Complete Technical Formulation.

This technical supplement presents the complete quantum‑gravity formulation of the Universal Model Framework (UMF) through eight rigorously validated protocols (QD‑01 to QD‑08). The framework constructs quantum dynamics on prime‑indexed distinction graphs, establishing a gauge‑invariant Hilbert space \mathcal{H_{\mathnormal{G}}}=L^2(U(1)^{N_E}), canonical commutation relations, and a prime‑weighted Hamiltonian whose continuum limit reproduces Einstein’s field equations. The formulation resolves the problem of time via deparametrization, provides coherent semiclassical states saturating \Delta A\Delta E=\hbar /2, and demonstrates UV‑finite renormalization with a stable fixed point preserving holographic scaling \eta =2.000\pm 0.003. Physical observables—including discrete area spectrum, curvature operators, graviton propagators, and entanglement entropy—are derived explicitly. Phenomenological predictions remain consistent with current constraints from GW170817, Planck CMB data, and precision Lorentz tests. This establishes UMF as a mathematically complete, experimentally testable quantum‑gravity theory grounded in prime‑indexed information geometry. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.