Bibliographic record
Abstract
Interpolatory and non-interpolatory multivariate Hermite type subdivision schemes are introduced in [8, 7]. In their applications in free-form surfaces, symmetry properties play a fundamental role: one can essentially argue that a subdivision scheme without a symmetry property simply cannot be used for the purpose of modelling free-form surfaces. The symmetry properties defined in the article [8] are formulated based on an underlying conception that Hermite data produced by the subdivision process is attached exactly to the vertices of the subsequently refined tessellations of the Euclidean space. As such, certain interesting possibilities of symmetric Hermite subdivision schemes are disallowed under our vertex-based symmetry definition. In this article, we formulate new symmetry conditions based on the conception that Hermite data produced in the subdivision process is attached to the faces instead of vertices of the subsequently refined tessellations. New examples of symmetric faced-based schemes are then constructed. Similar to our earlier work in vertex-based interpolatory and non-interpolatory Hermite subdivision schemes, a key step in our analysis is that we make use of the strong convergence theory of refinement equation to convert a prescribed geometric condition on the subdivision scheme – namely, the subdivision
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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".