On spin irreps of (1 I<sub><i>i</i></sub> 3) 12-fold uniform NMR spin systems as invariant-based dual tensorial sets: Roles in spin physics for weight sets and their -partitional frequency catalogues
Bibliographic record
Abstract
A direct systematic approach is given to the derivation of outer M-labelled {|IM(.)>} dual (spin) irrep sets for identical n [Formula: see text] 12-fold higher Ii nuclear spin ensembles, stressing (i) the essential role of multipartite partitions in spin physics, (ii) the value of algorithmic tableaux-based decompositions in the subsequent [Formula: see text]n combinatorical modelling, and (iii) how the dual group invariants (based on time-reversal invariance) govern the auxiliary labels of specialized dual tensors. Such (uniform inner rank) dual group basis sets (spin representations) underlie both NMR and isotopomer CNP spectral weightings. Specific applications are discussed here to illustrate the value of number partitional-based designs for statistical frequencies and recent algorithmic "sst" ([Formula: see text]n)-encoding techniques in quantized spin physics of uniform higher spin sets. In addition, a democratic recoupled form of purely SU(2) × [Formula: see text]2n projective modelling for the dual group invariants (SI) is given via an augmented democratic form of Weyl time-reversal invariance (TRV), over some regular solid geometry. From simple lattice-point geometric constraints, a maximal (2n)-index limit is established for global NMR ensemble spin symmetry. PACS Nos.: 02.10De, 02.20-a, 05.36Ch, 11.30Er, 33.25+k, 33.20Vq
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 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".