From the Balmer Limit to the Observable-Universe Scale: A Recursive Inversion of the Hydrogen Spectrum

This paper develops a recursive interpretation of the hydrogen Balmer series in which the
Balmer-limit wavelength is treated as one completed physical cycle rather than only as the
inverse of a spectral wavenumber. The normalized Balmer relation is written as a completed
fraction of this unit, while its inverse is interpreted as an infinite return series. The completed
spectral scale is then carried into a second, gravitational tier by repeating the same basic oper-
ations: normalization, inversion, and division at the level-2 boundary