Atomic emission spectra encode physical structure through observable photon energies, yetthe inverse mapping from spectra to atomic configuration is inherently information-entropic.In this work, we empirically assess which aspects of atomic quantum structure are recover-able from spectral observables alone and which are irretrievably compressed under radiativeprojection by quantifying information retention and loss. Using the NIST Atomic SpectraDatabase, we first demonstrate near-perfect statistical recovery of the Planck–Einsteinrelation, establishing a baseline for invertible physical structure. We then show that globalreconstruction of Moseley–Rydberg scaling fails decisively for neutral multi-electron atoms, re-flecting genuine degeneracy rather than model inadequacy. Constrained neural network modelsare subsequently used as diagnostic probes of information content, revealing a clear hierarchyof recoverability: initial-state quantum numbers exhibit statistically significant recoverabil-ity in restricted atomic regimes, while final-state quantum numbers are generally unstableand non-invertible, collapsing toward chance under mixed-element conditions. These resultsdemonstrate that radiative emission preserves only partial and regime-dependent informationabout atomic structure, with systematic loss increasing under electronic screening and config-uration mixing.
Cameron Gattis (Tue,) studied this question.