Bibliographic record
Abstract
Let s∈+r be a Levi decomposable Lie algebra, with Levi factor s, and radical r. A module V of s∈+r is cyclic indecomposable if it is indecomposable and the quotient module V/r·V is a simple s-module. A Levi decomposable subalgebra of a semisimple Lie algebra is cyclic wide if the restriction of every simple module of the semisimple Lie algebra to the subalgebra is cyclic indecomposable. We establish a condition for a regular Levi decomposable subalgebra of a semisimple Lie algebra to be cyclic wide. Then, in the case of a regular Levi decomposable subalgebra whose radical is an ad-nilpotent subalgebra, we show that the condition is necessary and sufficient for the subalgebra to be cyclic wide. All Lie algebras, and modules in this article are finite-dimensional, and over the complex numbers.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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 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".