A resolution of the Kohayakawa--Kreuter conjecture for the majority of cases
Bibliographic record
Abstract
For graphs $G, H_1,\dots,H_r$, write $G \to (H_1, \ldots, H_r)$ to denote the property that whenever we $r$-colour the edges of $G$, there is a monochromatic copy of $H_i$ in colour $i$ for some $i \in \{1,\dots,r\}$. Mousset, Nenadov and Samotij proved an upper bound on the threshold function for the property that $G(n,p) \to (H_1,\dots,H_r)$, thereby resolving the $1$-statement of the Kohayakawa--Kreuter conjecture. %We show that to prove the $0$-statement it suffices to prove a deterministic colouring result, which says that if $G$ is not too dense then $G \not \to (H_1,\dots,H_r)$. We extend upon the many partial results for the $0$-statement, by resolving it for a large number of cases, which in particular includes (but is not limited to) when $r \geq 3$, when $H_2$ is strictly $2$-balanced and not bipartite, or when $H_1$ and $H_2$ have the same $2$-densities.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.004 | 0.005 |
| Scholarly communication | 0.005 | 0.011 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.014 | 0.002 |
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 source (direct Gemma or distilled Codex), 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".