Supplementary Data and Code for Universal Nonlinear Scaling of Quantum Tunneling Splitting

We establish a universal nonlinear scaling law governing quantum tunneling splittings. Across canonical double-well systems, random-matrix ensembles, driven chaotic wells, and cooperative two-proton transfers, we demonstrate that $\ln \Delta E \propto -\sqrt{\mu_{\text{eff}}}$. This law is independent of dimensionality, potential form, and external driving. It positions tunneling as a paradigmatic nonlinear transport process, unifying phenomena from molecular isotope effects to chaotic Floquet dynamics under a single scaling archetype. The repository contains the full PRL manuscript (RevTeX source), Supplemental Material, and all figures (main + SI), along with reproducible scripts and data files.