SOME CONJECTURED UNIFORMLY OPTIMAL RELIABLE NETWORKS
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Bibliographic record
Abstract
We consider all-terminal reliability, one of the more popular models in the field of network reliability. A graph with n nodes and e edges, where the nodes are perfectly reliable and the edges survive independently with equal probability p , is said to be a uniformly optimally reliable graph if it has for all values of p (0 ≤ p ≤ 1) an equal or higher reliability among all graphs with the same number of nodes and edges. Boesch et al. [4] verified the existence of uniformly optimally reliable graphs for e = n − 1, e = n , e = n + 1, and e = n + 2; he has also given a conjecture for e = n + 3. Wang [8] proved this conjecture. In this article, we present four new infinite families of graphs that we conjecture to be uniformly optimal.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 it