A Novel Hydrogenic Superinvariant for Precision Tests of Quantum Electrodynamics

Abstract We present a hydrogenic superinvariant, which is a linear combination of optical transition frequencies designed to cancel the dominant Bohr, Dirac, and Lamb-shift contributions. This cancellation leaves sensitivity only to higher-order quantum electrodynamics (QED) and nuclear effects. Using Z-invariant spectral scalings and purely geometric angular factors, we identified dimensionless ratios that remain stable across different atomic species and guided the design of the superinvariant. The superinvariant is defined as: minus seven times the frequency of the 4→2 Balmer transition, plus seventeen times the frequency of the 5→2 transition, minus twenty-nine times the frequency of the 10→2 transition, plus nineteen times the frequency of the 20→2 transition. This construction cancels all contributions up to order one over n cubed. A digital experiment using CODATA constants and NIST tabulated values verifies cancellation at the level of one part in 10^14. The residual for hydrogen is about 2.3 kilohertz, while the scaling law S(Z) proportional to Z to the sixth power predicts, for example, about 1.47 × 10^5 hertz for singly ionized helium. A measurement with kilohertz accuracy using optical frequency combs would therefore provide a stringent and falsifiable test of bound-state QED.