Bibliographic record
Abstract
The PR-tree data structure is introduced to characterize the sets of path-tree models of path graphs. We further characterize the sets of directed path-tree models of directed path graphs with a slightly restricted form of the PR-tree called the Strong PR-tree. Additionally, via PR-trees and Strong PR-trees, we characterize path graphs and directed path graphs by their Split Decompositions. Two distinct approaches (Split Decomposition and Reduction ) are presented to construct a PR-tree that captures the path-tree models of a given graph G = (V, E) with n = |V| and m = |E|. An implementation of the split decomposition approach is presented which runs in O (nm) time. Similarly, an implementation of the reduction approach is presented which runs in O (A(n + m) nm) time (where A(s) is the inverse of Ackermann's function arising from Union-Find [40]). Also, from a PR-tree, an algorithm to construct a corresponding Strong PR-tree is given which runs in O (n + m) time. The sizes of the PR-trees and Strong PR-trees produced by these approaches are O (n + m) with respect to the given graph. Furthermore, we demonstrate that an implicit form of the PR-tree and Strong PR-tree can be represented in O (n) space.
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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".