Strong-majority bootstrap percolation on regular graphs with low\n dissemination threshold
Bibliographic record
Abstract
Consider the following model of strong-majority bootstrap percolation on a\ngraph. Let r be some positive integer, and p in [0,1]. Initially, every vertex\nis active with probability p, independently from all other vertices. Then, at\nevery step of the process, each vertex v of degree deg(v) becomes active if at\nleast (deg(v)+r)/2 of its neighbours are active. Given any arbitrarily small\np>0 and any integer r, we construct a family of d=d(p,r)-regular graphs such\nthat with high probability all vertices become active in the end. In\nparticular, the case r=1 answers a question and disproves a conjecture of\nRapaport, Suchan, Todinca, and Verstraete (Algorithmica, 2011).\n
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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".