Why this work is in the frame
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Bibliographic record
Abstract
In this paper, we study the existence of unavoidable 2-edge-colored patterns in edge-colorings of the complete graph. We are interested in how these patterns change as the densities of the color classes change. A graph is called balanceable if it can be found, with half its edges in one color and half of them in the other, in any 2-edge-coloring of Kn with sufficiently many edges in each color class and n large enough. The balancing number bal(n,G) of a balanceable graph G is the maximum number m of edges such that there is a coloring of Kn with m edges in one color class without having a balanced copy of G. Equivalently, any 2-edge-coloring of Kn with more than bal(n,G) edges in each color contains a balanced copy of G. Graphs with constant (not depending on n) balancing number have been previously characterized. We give a new proof of such characterization that allows us not only to understand in a deeper way the structure of the graphs with constant balancing number but also to show that bal(n,G) is quadratic on the number of edges of G, a bound that differs substantially from the previous known that was exponential.
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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 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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