Improved upper and lower bounds fork-broadcasting
Why this work is in the frame
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Bibliographic record
Abstract
We continue the investigation of k-broadcasting, a variant of broadcasting in which an informed vertex can call up to k of its neighbors in each time unit. A focus of the investigation into broadcasting is the function Bk(n), which is the minimum number of edges in any n vertex graph such that each vertex can originate a k-broadcast that completes in minimum time. We give several methods to construct graphs which allow minimum-time k-broadcasting from each vertex. These constructions give improvements to the best current upper bounds on Bk(n). We also give an improvement to the best existing lower bound on Bk(n). In addition, a few new exact values of Bk(n) are determined. © 2001 John Wiley & Sons, Inc.
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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 | 0.000 | 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 | 0.001 | 0.001 |
| 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