Empirical status of the hydrogen spectrum on this pair: pending spectroscopy evidence and the limits of the model's spectral statements

What the pair's spectral statements are. The model's content is the conditional spectral statement of The one-centre Coulomb model: bound energies, n^2-degeneracy, completeness of the bound states in the negative spectral subspace and the continuum: bound energies $E_n=-\frac{m{\kappa }^2}{2{\mathrm{\hslash }}^2{n}^2}$ with $n^2$-fold model degeneracy, a complete negative spectral subspace and a nonzero continuum, together with the two-body threshold reading of The declared two-body Coulomb model: reduced-mass decomposition, relative levels as thresholds and the absence of stationary total states. These are statements about the declared model and its assigned parameters; they are not statements about any measured hydrogen line.

Why no experiment appears on this pair. The design reservation for this pair names a spectroscopy data candidate and marks it pending. No source-backed observation record with preparation, apparatus, calibration, sampling and uncertainty was harvested for this batch, so no experiment item is built and no measured wavelength, frequency or transition is reported. The source treatments do describe the Lyman, Balmer, Paschen and Brackett series and the historical Balmer fit; this page neither reproduces their numerical values nor treats them as its own observations, and the comparison of the model with measured spectra is deferred to a future experiment item carrying its own uncertainty record.

What a comparison would presuppose. An emission-frequency illustration, conditional on an initial model energy $E_i$ greater than the final energy $E_f$, uses $\nu =(E_i-E_f)\mathrm{/}h$ together with the radiation extension and the light-matter coupling of later pairs; no transition-frequency claim is made on this page. Any comparison with a measured line would test the combined model, apparatus and constant assumptions: the preparation and isolation idealization, the identification of the species parameters with measured masses and charges, the treatment of linewidth, Doppler and instrumental response, and the sampling model of the recorded sample. Agreement of a finite set of measured lines with the predicted values would be evidence about the combined assumptions; it would not be a deductive proof of the model, and disagreement would require the same auxiliary assumptions to be examined before the model is rejected.

Excluded corrections and their status. The gross-structure model omits spin, relativistic fine structure, finite nuclear size, QED corrections including the Lamb shift, hyperfine structure and shielding, as recorded in The declared Coulomb and two-body hydrogen model: one-centre operator, relative problem, reduced mass and scope exclusions clause (f); the source treatments describe some of these corrections and their consequences, but no magnitude, splitting or numerical value is asserted or used by this pair.

Identification caution. The assignment of the model's parameters to a laboratory hydrogen atom is the tested identification of clause (e) of the model definition under the preparation and apparatus postulate (Preparation and apparatus postulate P7: declared preparations, isolation and sampling assumptions); it is not derived from the mathematics of the model and carries the uncertainty of that identification. The model's spectral statements remain conditional until such an identification, with its qualifications, is supplied.