Bibliographic record
Abstract
Airy functions are named after the English astronomer George Biddell Airy (1801–1892). Airy’s first mathematical work was on the diffraction phenomenon, namely, the Airy disk - the image of a point object by a telescope - which is familiar to all of us in optics. The name Airy is connected with many physical phenomena and includes, besides the Airy disk, the Airy spiral, an optical phenomenon visible on quartz crystals, and the Airy stress function in elasticity. Airy was very interested in optics and in fact studied the formation of rainbows. A good qualitative summary of the rainbow is given by Adam. In this paper Adam shows how the optical rainbow can be studied at many levels: (i) geometrical optics (rays), (ii) the Airy approximation, (iii) Mie scattering, (iv) complex angular momentum, and (v) catastrophe theory. Airy’s analysis is approximate but applies well to large raindrops that make up the common rainbow (for small drops, catastrophe theory has been used). Details of Airy’s analysis can be found in the chapter on the optics of raindrops in the book by van de Hulst (see also Berry). Airy also analyzed the intensity of light near a caustic wavefront.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.048 | 0.026 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".