Bibliographic record
Abstract
We study a class of bi-Lipschitz-invariant dimensions that range between the box and Assouad dimensions. The quasi-Assouad dimensions and \theta -Assouad spectrum are other special examples. These dimensions are localized, like Assouad dimensions, but vary in the depth of scale which is considered, thus they provide very refined geometric information. Our main focus is on the intermediate dimensions which range between the quasi-Assouad and Assouad dimensions, complementing the \theta -Assouad spectrum which ranges between the box and quasi-Assouad dimensions. We investigate the relationship between these and the familiar dimensions. We construct a Cantor set with a non-trivial interval of dimensions, the endpoints of this interval being given by the quasi-Assouad and Assouad dimensions of the set. We study stability and continuity-like properties of the dimensions. In contrast with the Assouad-type dimensions, we see that decreasing sets in \mathbb{R} with decreasing gaps need not have dimension 0 or 1. As is the case for Hausdorff and Assouad dimensions, the Cantor set and the decreasing set have the extreme dimensions among all compact sets in \mathbb{R} whose complementary set consists of open intervals of the same lengths.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| 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; both teacher heads agree on what is shown here.
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".