Bibliographic record
Abstract
A triquadratic number field is a number field of degree 8 that is created by adjoining the square roots of three rational, squarefree integers to Q. We often denote a number field by K and its ring of integers by O_K. The ring of integers is defined to be the set of all elements of K that are zeros of a monic polynomial with coefficients in Z. It is already well-known that the ring of integers for a quadratic field Q(a) is given by all integer linear combinations of either {1, √a} or {1, (1+√a)/2 } depending on the value of a. These sets are called an integral basis for the ring of integers of the number field Q(a). The integral bases for the rings of integers for biquadratic fields are also already known. In Chatelain’s paper he provides all of the information necessary to deter- mine the bases for all n-quadratic fields, but they are not presented in an explicit format. In this paper, we look at results of Chatelain and use these to determine more concise integral bases for triquadratic fields.
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".