Recursive calculation of nonprimitive coupling and recoupling brakets
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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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it