Bibliographic record
Abstract
Bose et al. [P. Bose et al., Guarding polyhedral terrains, Comput. Geom., Theory Appl. 6 (1997), pp. 173–185.] proved that ⌊ (4n−4)/13 ⌋ edge guards are sometimes necessary to guard an n-vertex polyhedral terrain. Subsequently, Kaučič et al. [B. Kaučič, B. Žalik, and F. Novak, On the lower bound of edge guards of polyhedral terrains, Int. J. Comput. Math. 80 (2003), pp. 811–814.] claimed to find an inconsistency in the proof and used Bose et al. ’s proof technique to prove a weaker lower bound of ⌊ (2n−4)/7 ⌋ edge-guards. They declared that a proof of the original lower bound of ⌊ (4n−4)/13 ⌋ remains an open issue. The purpose of this note is simply to point out that the issue is not open and that Bose et al. ’s original proof is correct. We present the original proof of ⌊ (4n−4)/13 ⌋ at a level of detail to hopefully remove any misunderstanding of the result.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.039 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.005 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.004 | 0.009 |
| Scholarly communication | 0.005 | 0.017 |
| Open science | 0.008 | 0.009 |
| Research integrity | 0.003 | 0.025 |
| Insufficient payload (model declined to judge) | 0.013 | 0.003 |
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 source (direct Gemma or distilled Codex), 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".