Bibliographic record
Abstract
This paper introduces a pioneering concept in the realm of metric spaces, specifically focusing on a novel category termed controlled generalized b-metric spaces (CGbMS). The study delves into the investigation of fixed points within CGbMS for self-mappings that exhibit both linear and non-linear contraction characteristics. The analysis establishes the existence and uniqueness of such fixed points, contributing valuable insights into the properties of these spaces. Moreover, the paper extends its impact by exploring diverse applications and implementations derived from the established results. One notable application is the application of these findings in solving systems of linear equations. The comprehensive examination of these applications not only underscores the practical significance of the proposed concept but also offers a broader understanding of its potential utility in various mathematical contexts. In summary, this research not only introduces and rigorously defines the concept of controlled generalized b-metric spaces but also provides a robust theoretical foundation by establishing the existence and uniqueness of fixed points. The exploration of applications, with a focus on solving linear equations, further highlights the practical implications and versatility of the proposed framework within the broader mathematical landscape.
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How this classification was reachedexpand
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 | 0.002 | 0.002 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".