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 machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".