Twisted spin Sutherland models from quantum Hamiltonian reduction
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Bibliographic record
Abstract
Recent general results on Hamiltonian reductions under polar group actions are applied to study some reductions of the free particle governed by the Laplace-Beltrami operator of a compact, connected, simple Lie group. The reduced systems associated with arbitrary finite dimensional irreducible representations of the group by using the symmetry induced by twisted conjugations are described in detail. These systems generically yield integrable Sutherland type many-body models with spin, which are called twisted spin Sutherland models if the underlying twisted conjugations are built on non-trivial Dynkin diagram automorphisms. The spectra of these models can be calculated, in principle, by solving certain Clebsch-Gordan problems, and the result is presented for the models associated with the symmetric tensorial powers of the defining representation of SU(N). 1 1
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| 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