Prime-Indexed Quantum Coherence - Empirical Validation of UMF Predictions

We present the first comprehensive empirical validation of quantum coherence enhancement on prime-indexed fractal lattices, as predicted by the Universal Model Framework (UMF). Using extensive numerical simulations of classical random walks, continuous-time quantum walks (CTQW), and discrete-time quantum walks (DTQW) on Sierpiński triangle structures, we show that prime-modulated quantum transport exhibits significantly enhanced localization properties compared to standard quantum walks. Our results demonstrate that prime-filtering mechanisms in quantum walk dynamics generate sustained return probabilities and non-trivial transport signatures that persist across extended time scales. Baseline validation is provided by classical diffusion on fractal substrates, with walk dimension dw≈5.26d_w \approx 5.26dw≈5.26 and spectral dimension ds≈0.60d_s \approx 0.60ds≈0.60. These findings constitute the first direct empirical evidence for UMF predictions that prime number sequences encode fundamental geometric constraints on quantum coherence. This establishes a novel connection between number theory and quantum transport phenomena, offering testable predictions for future quantum information experiments. This project was developed by Marco Gericke, with structured assistance from a large language model (Perplexity). 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.