Identify a pattern with multiple lines

Preserve the ambiguity before adding evidence

Select record A with only its first feature revealed. The supplied center is 388.90 nm. It is close to both a selected hydrogen reference at 388.9049 nm and a helium reference at 388.86489 nm. Before revealing another feature, write both candidates in your notebook.

Compute signed residuals as supplied center minus reference. For hydrogen the residual is −0.00490 nm; for helium it is +0.03511 nm. Both absolute differences are smaller than the stipulated 0.10 nm tolerance. The closer numerical match does not automatically become a unique identification: the model retains every compatible candidate instead of inventing a probability ranking.

The selected source wavelengths are from the air sections of the NIST hydrogen and helium tables. They identify specific listed transitions rather than calculated centroids of neighboring components. The exercise does not model resolved multiplet shapes.

Use a second feature to test the hypothesis

Reveal all recorded features in A. The second center is 486.13 nm, close to the selected H I reference 486.12786 nm. Its residual is +0.00214 nm. The selected helium references cannot explain this second feature, so hydrogen remains the compatible single-species candidate under the stated comparison.

Now inspect B. Its first feature, 388.88 nm, is also compatible with both nearby references. Its second feature is 447.15 nm, matching the He I reference 447.1479 nm with residual +0.00210 nm. The added evidence selects a different compatible single-species hypothesis.

Make a two-row paper ledger for each case. Include raw center, candidate reference, signed residual and pass/fail against the tolerance. Capture the ambiguous state before the additional feature. Otherwise, a final candidate list can hide the reasoning that made the second observation useful.

Define exactly what compatibility means

The question is whether every revealed feature can be associated with a distinct selected transition of one listed neutral species. A feature cannot borrow one transition twice to explain two separate observed features. This one-to-one assignment requirement prevents duplicate use of the same reference from creating false multi-line support.

The candidate universe is small: H I, He I and Na I, with only eight selected reference wavelengths altogether. Compatibility is not a proof that the source contains only that element. Failure means the particular selected-line single-species hypothesis does not explain every revealed feature, not that the species is absent from the source.

There is also no requirement that every reference transition appear in the supplied record. The listed features are selected reports, not a complete detection inventory. An unreported line must not be treated as a verified nondetection, even when its wavelength lies within the covered interval.

Check another pattern and the units

Record C supplies 589.00 and 589.59 nm. Compare these with selected Na I references 588.9950 and 589.5924 nm. The residuals are +0.00500 and −0.00240 nm, so two distinct selected sodium transitions explain the pair within tolerance. NIST sodium references.

The tolerance is an authored rule for simplified records. It is neither a confidence interval nor the precision of the reference source. Perform comparisons using the full listed values rather than rounding everything to one decimal place first. Rounding near a tolerance boundary can change a decision.

At stages before calibration is revealed, these comparisons assume zero offset provisionally. A pattern that becomes incompatible after adding evidence cannot regain compatibility simply by ignoring the inconvenient line. A separately supported calibration correction is a different operation, explored next.

Transfer to a new supplied pair

A paper record has independently confirmed zero offset and centers 434.05 and 486.12 nm. Compare them with the selected hydrogen references 434.0462 and 486.12786 nm. Do both pass, and what claim remains too strong?