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
Let $I$, $H$, $S$, $P$, $P_s$ be the usual operators on classes of rings: $I$ and $H$ for isomorphic and homomorphic images of rings and $S$, $P$, $P_s$ respectively for subrings, direct, and subdirect products of rings. If $\mathcal K$ is a class of commutative rings with identity (and in general of any kind of algebraic structures), then the class $HSP({\mathcal K})$ is known to be the variety generated by the class $\mathcal K$. Although the class $SHPS({\mathcal K})$ is in general a proper subclass of the class $HSP({\mathcal K})$ for many familiar varieties $HSP({\mathcal K})= SHPS({\mathcal K})$. Our goal is to give an example of a class $\mathcal K$ of commutative rings with identity such that $HSP({\mathcal K})\not = SHPS({\mathcal K})$. As a consequence we will describe the structure of two partially ordered monoids of operators.
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 | 0.000 | 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 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| 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