Fixed-Point Results for Mappings Satisfying Implicit Relation in Orthogonal Fuzzy Metric Spaces
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Bibliographic record
Abstract
This research paper introduces a comprehensive study on fixed points in orthogonal fuzzy metric spaces. The primary objective is to establish the existence and uniqueness of fixed points for self-mappings satisfying implicit relation criteria in complete orthogonal fuzzy metric spaces. By doing so, our proven results extend and generalise well-known findings in the field of fixed-point theory. To demonstrate the significance of the established results, several related examples are provided, serving to support and validate the theoretical findings in orthogonal fuzzy metric spaces. The implications of these results are discussed, shedding light on their potential applications in various practical scenarios. In addition to theoretical advancements, the paper also demonstrates a practical application of our established results in solving integral equations. This application exemplifies the effectiveness and versatility of the proposed approach in real-world problem-solving scenarios.
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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 | 0.003 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.004 |
| 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 | 0.000 |
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