Statistical Convergence with Rough I3-Lacunary and Wijsman Rough I3-Statistical Convergence in 2-Normed Spaces
Bibliographic record
Abstract
In this paper, we have introduced the concept of the set of rough I3-lacunary limit points for triple sequences in 2-normed spaces. We have established statistical convergence requirements associated with this set. Furthermore, we have introduced the idea of rough I3-lacunary statistical convergence for triple sequences. Additionally, we have demonstrated that this set of rough I3-lacunary limit points is both convex and closed within the context of a 2-normed space. We have also explored the relationships between a sequence’s rough I3-lacunary statistical cluster points and its rough I3-lacunary statistical limit points in the same 2-normed space. Expanding upon the concept of triple sequence spaces, we have introduced the notion of Wijsman I3-Cesáro summability for triple sequences. In doing so, we have investigated the connections between Wijsman strongly I3-Cesáro summability and Wijsman statistical I3-Cesáro summability. Furthermore, we have introduced the concepts of Wijsman rough strongly p-lacunary summability of order α and Wijsman rough lacunary statistical convergence of order α for triple sequences. These new concepts have been subjected to a thorough examination to understand their characteristics, and we have explored potential connections between them. Additionally, we have investigated how these newly introduced concepts relate to existing notions in the literature.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.005 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), 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".