Rotationally Monotone Polygons.
Bibliographic record
Abstract
A generalization of monotonicity is introduced. An n-vertex polygon P is rotationally monotone w.r.t. a point r if there exists a partitioning of the boundary of P into exactly two polygonal chains, s.t. one chain can be ro-tated clockwise around r and the other chain can be rotated counterclockwise around r with neither chain intersecting the interior of the polygon. We present the following two results: (1) Given P and a center of rota-tion r in the plane, we determine in O(n) time whether P is rotationally monotone w.r.t. r. (2) We can find all the points in the plane from which P is rotation-ally monotone in O(n) time for convex polygons and in O(n2) time for simple polygons. Both algorithms are worst-case optimal. 1
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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".