Bibliographic record
Abstract
Abstract. The possible pivot operations of the simplex method to solve a linear program can be represented as a directed graph defined on the skeleton of the feasible region P. We consider the case that P is bounded, i.e., a convex polytope. The directed graph is called an LP digraph. LP digraphs are known to satisfy the following three properties: acyclicity, unique sink orientation (USO), and the Holt–Klee property. The three properties are not generally sufficient for a directed graph on the skeleton of P to be an LP digraph. In this paper, we first survey some previous results on LP digraphs, showing relationships among the three properties. Then we introduce a new necessary property for a directed graph on the skeleton of P to be an LP digraph, called the shelling property. We analyze the relationships between the shelling property and the three existing properties, showing that it is stronger than a combination of acyclicity and USO for nonsimple polytopes in dimension at least four. In all other cases it is equivalent to the intersection of these two properties. 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".