Reproducible Code and Data for "Numerical Upper Bounds for Planar k-Fold Disk Coverings in Restricted Lattice and Two-Translate Families"

This record provides the full reproduction package (code, scripts, and numerical outputs) for the study “Numerical Upper Bounds for Planar k-Fold Disk Coverings in Restricted Lattice and Two-Translate Families.” The package implements a deterministic grid-sampling estimator over a fundamental domain and a Lipschitz-based discretization correction to produce certified upper bounds on k-fold covering radii and induced density intervals. Experiments cover baseline lattices A2 and Z2 (D2 ≡ Z2 in 2D) for k ∈ {1,2,3}, as well as a two-translate family X = A2 ⊎ (A2 + t) with shift optimization at k = 2. Included are reproduction scripts, configuration files (grid resolution N, neighbor-box parameter M), validation diagnostics (coverage checks, neighbor completeness, grid refinement, shift invariance), and generated tables/figures corresponding to the manuscript (e.g., Table 1 and Figures 1–3).