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Build record verified 2026-10-28.
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Radial one-dimensional boundary-value eigenproblem solved by finite elements. The demo checks the six n<=3 hydrogen Coulomb energies; no claim of validating the relativistic or self-consistent DFT paths. Dedicated I1b driver checks 12 nonrelativistic Coulomb energies for Z=1,2 and n<=3, including angular degeneracies, against -Z^2/(2*n^2) Hartree. First-six returned wavefunctions are checked only for finiteness. Dirac/DFT branches, wavefunction normalization and full-spectrum accuracy are not verified.