On the module structure of the center of hyperelliptic Krichever–Novikov algebras II
Bibliographic record
Abstract
Let R=C[t±1,u:u2=t(t−α1)⋯(t−α2n)], corresponding to a nonsingular hyperelliptic curve. Let g⊗R be the corresponding current Lie algebra. The universal central extension of g⊗R is ĝ=g⊗R⊕ΩR/dR, where ΩR/dR is a module over Aut(R). In earlier work, Cox–Im described how ΩR/dR decomposes into a direct sum of irreducible representations when Aut(R) was the cyclic group C2k or the dihedral group D2k. In this paper, we precisely determine Aut(R), giving examples of 2n-tuples (α1,…,α2n) when Aut(R) is Gn=Dicn,Un≅D2n, or Un (n even). We then describe the decomposition of ΩR/dR when Aut(R) is D2k.
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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 | 0.000 | 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 | 0.002 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".