Sp(1)-symmetric hyperkählerquantisation
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Bibliographic record
Abstract
We provide a new general scheme for the geometric quantisation of Sp(1)- symmetric hyperkahler manifolds, considering Hilbert spaces of holomorphic sections with respect to the complex structures in the hyperkahler 2-sphere. Under properness of an associated moment map, or other finiteness assumptions, we construct unitary (super) representations of groups acting by Riemannian isometries preserving the 2-sphere, and we study their decomposition in irreducible components. We apply this scheme to hyperkahler vector spaces, the Taub–NUT metric on R4, moduli spaces of framed SU(r)-instantons on R4, and in part to the Atiyah–Hitchin manifold of magnetic monopoles in R3.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.002 |
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