Bibliographic record
Abstract
Abstract To each field F of characteristic not 2, one can associate a certain Galois group , the so-called W-group of F , which carries essentially the same information as the Witt ring W ( F ) of F . In this paperwe investigate the connection between and (√a), where F (√a) is a proper quadratic extension of F . We obtain a precise description in the case when F is a pythagorean formally real field and a = −1, and show that the W-group of a proper field extension K/F is a subgroup of the W-group of F if and only if F is a formally real pythagorean field and K = F (√−1). This theorem can be viewed as an analogue of the classical Artin-Schreier’s theorem describing fields fixed by finite subgroups of absolute Galois groups. We also obtain precise results in the case when a is a double-rigid element in F. Some of these results carry over to the general setting.
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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 | 0.001 |
| 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) | 0.005 | 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".