Why this work is in the frame
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Bibliographic record
Abstract
Suppose a group $$\Gamma $$ acts on a scheme $$X$$ and a Lie superalgebra $$\mathfrak {g}$$ . The corresponding equivariant map superalgebra is the Lie superalgebra of equivariant regular maps from $$X$$ to $$\mathfrak {g}$$ . We classify the irreducible finite dimensional modules for these superalgebras under the assumptions that the coordinate ring of $$X$$ is finitely generated, $$\Gamma $$ is finite abelian and acts freely on the rational points of $$X$$ , and $$\mathfrak {g}$$ is a basic classical Lie superalgebra (or $$\mathfrak {sl}\,(n,n)$$ , $$n \ge 1$$ , if $$\Gamma $$ is trivial). We show that they are all (tensor products of) generalized evaluation modules and are parameterized by a certain set of equivariant finitely supported maps defined on $$X$$ . Furthermore, in the case that the even part of $$\mathfrak {g}$$ is semisimple, we show that all such modules are in fact (tensor products of) evaluation modules. On the other hand, if the even part of $$\mathfrak {g}$$ is not semisimple (more generally, if $$\mathfrak {g}$$ is of type I), we introduce a natural generalization of Kac modules and show that all irreducible finite dimensional modules are quotients of these. As a special case, our results give the first classification of the irreducible finite dimensional modules for twisted loop superalgebras.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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