Why this work is in the frame
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Bibliographic record
Abstract
A ring with involution ∗ is called ∗-clean if each of its elements is the sum of a unit and a projection. It is obvious that ∗-clean rings are clean. Vaš asked whether there exists a clean ring with involution that is not ∗-clean. In this paper, we investigate when a group ring RG is ∗-clean, where ∗ is the classical involution on RG. We obtain necessary and sufficient conditions for RG to be ∗-clean, where R is a commutative local ring and G is one of the groups C 3 , C 4 , S 3 and Q 8 . As a consequence, we provide many examples of group rings which are clean but not ∗-clean.
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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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it