Code and data for: Axial angular momentum protects the parity–time symmetric phase of a three-dimensional trap with a gain–loss dipole

R code and tabulated results reproducing every figure and table of the accompanying manuscript. The scripts solve the non-Hermitian radial eigenvalue problem for a three-dimensional isotropic harmonic trap perturbed by a pair of Gaussian gain and loss spots placed symmetrically on the symmetry axis, and locate the coupling at which the parity–time symmetric phase breaks. The deposit contains the core numerical routines, a validation suite including an exactly solvable limit, the threshold computation with full spectral monitoring, the exceptional-point and sensitivity checks, and the figure-generation scripts. Two tables are included: the converged thresholds reported in the manuscript, and the complete set of 21 parameter points including the nine discarded, with the coalescing pair and the truncation error recorded for each, so that the selection criterion can be audited. Everything runs in base R 4.3.3 with no external package.