Recursive calculation of nonprimitive coupling and recoupling brakets
Bibliographic record
Abstract
The concept of coupling coefficients of angular momentum for the rotation group chain [Formula: see text] can be extended to representations of any group-chain factorisation by defining the generalised notion of a braket. We give a unified approach to recoupling coefficients (rccs), vector-coupling coefficients (vccs), and 3j phases for all group-chain transformations. Category theory is the appropriate tool for studying the representations of groups and algebras. The explicit use of category theory leads to a new recursion scheme for the calculation of brakets. We derive specialisations for calculating nonprimitive rccs and nonprimitive vccs from primitive rccs, primitive vccs, and 3j phases. This new recursion scheme forms the algorithmic core of Racah v4. Racah v4 is a software package developed at the University of Canterbury to calculate group representation coefficients (brakets). PACS Nos.: 02.20.Mp, 03.65.Fd, 31.15.p, 31.15.Hz, 02.10.Ws
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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 | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".