Hydrogenic Alignment as a Coordinate Principle for Atomic Spectra (Clarifying note to RGAS)

This paper is a conceptual and methodological clarification of Recursive Geometry of Atomic Spectra (RGAS), emphasizing coordinate definition, empirical controls, and scope. Atomic spectra are typically analyzed in native variables such as wavelength, energy, and term labels, which can obscure global structure across ions. This white paper introduces hydrogenic alignment as a coordinate principle for spectral organization. Using the hydrogenic Rydberg scale as a reference and measuring level spacings by powers of the fine-structure constant α defines a continuous exponent coordinate γ (“hydrogenic alignment depth”). When experimentally measured photon frequencies are plotted against this levels-derived coordinate, a statistically significant subset of photons aligns along near-linear threads in the (γ, log₁₀ν) plane, with a universal slope β ≈ log₁₀α and ion-specific intercepts. The analysis follows a strictly non-circular, two-phase pipeline: γ is derived from energy levels alone, and photons are overlaid only post hoc. Density-preserving null models and false-discovery-rate control are used to assess statistical significance. This work does not propose a new Hamiltonian or claim that all spectral structure is hydrogenic. Rather, it demonstrates that hydrogen provides a useful organizing coordinate: a measurable subset of atomic spectra aligns to it, and residual (non-aligned) structure becomes more interpretable when expressed relative to this reference frame.