COMPUTING THE SET OF ALL THE DISTANT HORIZONS OF A TERRAIN
Why this work is in the frame
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Bibliographic record
Abstract
We study the problem of computing the set of all distant horizons of a terrain, represented as either: (1) the set of all edges that appear on the distant horizon from at least one viewing direction; (2) for every edge e, the set of direction intervals for which e appears on the distant horizon; or (3) a search structure to query for the edges on the distant horizon, or the precise distant horizon, from a fixed viewing direction. We describe an algorithm that solves the first and second forms of the problem in O(n 2+∊ ) time for any constant ∊ > 0 where n is the number of edges of the terrain. This algorithm can be extended to compute a search structure for (3) in O(n 2+∊ ) time. The search structure can return the s edges on the distant horizon in O( log n + s) time. We show solving problem (1) is 3SUM hard. Furthermore, we construct a terrain with a single local maximum in which Θ(n) edges each have Θ(n) direction intervals, showing that our solution to (2) cannot be significantly improved, in the worst case, even for such restricted terrains. This takes advantage of a novel construction in which the convex hull of a set of n linearly moving points, whose trajectories do not intersect, changes Ω(n 2 ) times.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 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 it