Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
A ring [Formula: see text] is an essential extension of its ideal [Formula: see text] if [Formula: see text], for every nonzero ideal [Formula: see text] of [Formula: see text]. Let [Formula: see text] be the prime radical. A class [Formula: see text] of prime rings that is closed under ideals and essential extensions is called a [Formula: see text]-class if [Formula: see text], where [Formula: see text] is the upper radical determined by [Formula: see text]. Let * be the class of all semiprime rings [Formula: see text] such that [Formula: see text] [Formula: see text] for every ideal [Formula: see text] of [Formula: see text] with [Formula: see text]. In this paper, we give some necessary and sufficient conditions for [Formula: see text] to be a [Formula: see text]-class. Intersections of [Formula: see text]-classes have always been found to be [Formula: see text]-classes and Leavitt asked whether this is always true. We show some of the strong restrictions which must apply to any possible counterexample.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| 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 | 0.001 | 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 it