Advanced Phyllotactic Quantum Analysis: Finite-Size Scaling, Boundary Locking, and Spectral Statistics

Building upon the foundational quantum properties of Golden Mean Vogel arrays, this complementary report investigates advanced topological and statistical behaviors within the aperiodic lattice. Through four targeted numerical experiments, we explicitly analyze the finite-size scaling of sub-diffusive transport, the bulk-boundary correspondence of geometric edge states, continuous spectral flow under synthetic magnetic fields, and global energy level spacing statistics. These empirical findings corroborate the presence of structurally protected localization regimes and highlight the architecture's inherent immunity to quantum decoherence.