Bibliographic record
Abstract
Abstract A common model of robustness of a graph against random failures has all vertices operational, but the edges independently operational with probability . One can ask for the probability that all vertices can communicate ( all‐terminal reliability ) or that two specific vertices (or terminals ) can communicate with each other ( two‐terminal reliability ). A relatively new measure is split reliability , where for two fixed vertices and , we consider the probability that every vertex communicates with one of or , but not both. In this article, we explore the existence for fixed numbers and of an optimal connected ‐graph for split reliability, that is, a connected graph with vertices and edges for which for any other such graph , the split reliability of is at least as large as that of , for all values of . Unlike the similar problems for all‐terminal and two‐terminal reliability, where only partial results are known, we completely solve the issue for split reliability, where we show that there is an optimal ‐graph for split reliability if and only if , , or .
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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".