Bibliographic record
Abstract
Given a prime \( p \), a \( p \)-{smooth} integer is an integer whose prime factors are all at most \( p \). Let \( S_p \) be the multiplicative subgroup of \( \mathbb{Q} \) generated by \(-1\) and the \( p \)-smooth integers. Define the \( p \)-{smooth} partial field as \( \mathbb{S}_p = (\mathbb{Q}, S_p) \). Let \( g \) be the golden ratio \( (1+\sqrt{5})/2 \). Let \( G_p \) to be the multiplicative subgroup of \( \mathbb{R} \) generated by \( g \), \(-1\), and the \( p \)-smooth integers. Define the \( p \)-{golden} partial field as \( \mathbb{G}_p = (\mathbb{R}, G_p) \). The partial field \( \mathbb{S}_2 \) is actually the well-known dyadic partial field and \( \mathbb{S}_3 \) has sometimes been called the Gersonides partial field. We calculate the fundamental elements of \( \mathbb{S}_5 \), \( \mathbb{G}_2 \), \( \mathbb{G}_3 \), and \( \mathbb{G}_5 \). Our proofs make use of the SageMath computational package.
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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 | 0.003 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 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".