Novel Investigations of m-Bi-Ideals and Generators in b-Semirings with Extended Operator Frameworks
Why this work is in the frame
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Bibliographic record
Abstract
In this study, we introduce novel types of m-quasi-ideals and m-bi-ideals in the context of b-semirings, expanding the scope of algebraic structures in this field. We provide detailed characterizations of these ideals, focusing on their distinct properties and interactions within b-semirings. Utilizing an algebraic approach, we elucidate the fundamental properties of m-bi-ideals, examining their behavior and structural role. Additionally, we explore the generators of m-bi-ideals and offer characterizations based on their relationship with bi-ideals. Our findings contribute to a deeper understanding of m-ideals and m-bi-ideals, opening new avenues for further research in algebraic theory and the study of semirings.
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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