Geodesic distance approximation using a surface finite element method for the p-Laplacian
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Bibliographic record
Abstract
We use the p -Laplacian with large p -values in order to approximate geodesic distances to features on surfaces. This differs from Fayolle and Belyaev's ( 2018 ) computational results using the p -Laplacian for the distance-to-surface problem. Our approach appears to offer some distinct advantages over other popular PDE-based distance function approximation methods. We employ a surface finite element scheme and demonstrate numerical convergence to the true geodesic distance functions. We check that our numerical results adhere to the triangle inequality and examine robustness against geometric noise such as vertex perturbations. We also present comparisons of our method with the heat method from Crane et al. (2017) and the classical polyhedral method from Mitchell et al. (1987) .
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.003 |
| 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)
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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