Bibliographic record
Abstract
Let F be a field of prime characteristic p containing 𝔽 p n as a subfield. We refer to q(X) = X p n - X - a ∈ F[X] as a generalized Artin–Schreier polynomial. Suppose that q(X) is irreducible and let C q(X) be the companion matrix of q(X). Then ad C q(X) has such highly unusual properties that any A ∈ 𝔤𝔩(m) such that ad A has like properties is shown to be similar to the companion matrix of an irreducible generalized Artin–Schreier polynomial. We discuss close connections with the decomposition problem of the tensor product of indecomposable modules for a one-dimensional Lie algebra over a field of characteristic p, the problem of finding an explicit primitive element for every intermediate field of the Galois extension associated to an irreducible generalized Artin–Schreier polynomial, and the problem of finding necessary and sufficient conditions for the irreducibility of a family of polynomials.
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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 | 0.000 | 0.000 |
| 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".