On Uniform (1≤<i>I</i><sub><i>i</i></sub>≤3) <i>n</i>‐fold {∣<i>I</i><sup>outer</sup><i>M</i>(<i>i</i><sub>1</sub>⋅⋅⋅<i>i</i><sub><i>n</i></sub>)〉} dual tensorial sets, spin irreps from <i>SU</i>(3≤<i>m</i>)×𝒮<sub><i>n</i></sub>⊃⋅⋅⋅⊃𝒮<sub><i>n</i></sub> weight sets: a direct role for 𝒩(λ⊢<i>n</i>)‐partitional catalogs of 𝒮<sub><i>n</i></sub> combinatorics in spin physics
Bibliographic record
Abstract
Abstract A direct systematic approach is given to the derivation of outer M ‐labeled ∣ IM (⋅)〉 dual (spin) irreps for identical higher nuclear spin ensembles. This stresses the essential role of multipartite partitions in spin physics and the value of algorithmic tableau‐based decompositions of 𝒮 n combinatorics. Additional purely 𝒮 n projective modeling techniques for the numbers of independant ensemble scalar invariants are discussed briefly. Such uniform inner rank dual group basis sets (spin representations) are as central to NMR as they are to all isotopomer CNP aspects of spectral weighting. Three specific applications are presented: one involving \documentclass{article}\pagestyle{empty}\begin{document}$[A]_{6}^{(I_{i})}$\end{document} systems, whereas the others treat 2 H‐cubane and the spin subensembles of the trans‐[ 2 H 11 B] 10 (CH 2 ) 2 carborane isotopomer to illustrate recent algorithmic roles specifically for “sst” (𝒮 n ) encoding in (quantized) spin physics and quantum‐Liouville NMR spin dynamics. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002
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How this classification was reachedexpand
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 | 0.005 | 0.003 |
| Meta-epidemiology (narrow) | 0.007 | 0.008 |
| Meta-epidemiology (broad) | 0.008 | 0.007 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.008 | 0.003 |
| Research integrity | 0.005 | 0.010 |
| Insufficient payload (model declined to judge) | 0.000 | 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; both teacher heads agree on what is shown here.
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".