ℤ<sub>2</sub>× ℤ<sub>2</sub>-symmetric spaces
Why this work is in the frame
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Bibliographic record
Abstract
The notion of a -symmetric space is a generalization of the classical notion of a symmetric space, where a general finite abelian group replaces the group ޚ 2 .We approach the classification of -symmetric space in the case = ޚ 2 × ޚ 2 using recent results on the classification of complex ޚ 2 × ޚ 2graded simple Lie algebras.The notion of a -symmetric space, introduced by R. Lutz [1981], is a generalization of the classical notion of a symmetric space, where a general finite abelian group replaces the group ޚ 2 .The case = ޚ k has also been studied, from the algebraic point of view by V. Kac [1968] and from the point of view of differential geometry by Ledger and Obata [1968], by Kowalski [1980] or by Wolf and Gray [1968] in terms of k-symmetric spaces.In this case, a k-manifold is a homogeneous reductive space and the classification of these varieties is given by the corresponding classification of graded Lie algebras.We approach the classification of -symmetric spaces in the case = ޚ 2 ޚ× 2 in a similar way, using recent results (see [Bahturin et al. 2005]) on the classification of complex ޚ 2 ޚ× 2 -graded simple Lie algebras.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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