Induced gauge stiffness, Hopf solitons, and the consistency of an ordered vacuum: a lattice study

Data and code for "Induced gauge stiffness, Hopf solitons, and the consistency of an ordered vacuum: a lattice study" (T. Riedel, 2026). This deposit contains the complete reproducibility package for the paper: every quantitative claim maps to a runnable script and its data via the included README_PACKAGE.md, and MANIFEST.json lists SHA256 checksums for all 54 files. Contents: (i) Python scripts for all computations — Monte Carlo of compact U(1) (phase scan, DeGrand–Toussaint monopole density, hot/cold metastability), exact determinant calculations of the induced Maxwell coupling (hopping validation and small-flux/twisted-boundary analysis), GPU (CuPy) relaxation of massive Faddeev–Skyrme hopfions with FIRE and topology guard, Hopf-charge measurement by two independent methods (Whitehead/FFT and preimage linking), axial-symmetry verification, collective inertia coefficients, the (c₄, m²) parameter scan, and continuum extrapolations; (ii) JSON result files for all runs; (iii) all paper figures; (iv) converged field checkpoints (.npz, fp64) for the Q_H = 1 solutions at three resolutions/volumes, the Q_H = 2 solution, and the full parameter scan; (v) the manuscript source. Key results reproducible from this package: the deconfinement threshold and first-order metastability of compact U(1); the quantitative obstruction to a purely induced Maxwell term; a validated Q_H = 1 hopfion with continuum mass E_cont = 1698.7(40); the scaling collapse E = √c₄·g(m²c₄) with Battye–Sutcliffe benchmark agreement at the half-percent level; and E(Q=2)/E(Q=1) = 1.597. Requirements: Python 3.11+, NumPy/SciPy (all analyses); CuPy with CUDA 12 for the GPU relaxation scripts (each has a --cpu fallback). All floating-point computations in fp64.