Bibliographic record
Abstract
The RacahWigner calculus is formulated using category theory. The notion of recoupling requires a consistent choice of isomorphisms corresponding to regrouping of irreducible representations. This is the essential content of a ring category. Hence the RacahWigner calculus is inherently a ring category. Category theory places the emphasis on maps between representations. The diagrammatic approach of category theory lays bare underlying relationships in the RacahWigner calculus. Direct sum decomposition, coupling coefficients, recoupling coefficients, and group chain decomposition are simplified and clarified when represented by diagrams. The diagram techniques of category theory are unlike diagram techniques used for group calculations. The BiedenharnElliott sum rule, Racah backcoupling, Racah factorisation lemma, and the WignerEckart theorem are derived from properties of this category. PACS Nos.: 02.10Ws, 02.20Qs, 02.20Fh, 02.20Df, 03.65Fd, 31.15Hz
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
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".