On Even-Degree Subgraphs of Linear Hypergraphs
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Bibliographic record
Abstract
A subgraph of a hypergraph H is even if all its degrees are positive even integers, and b - bounded if it has maximum degree at most b . Let f b ( n ) denote the maximum number of edges in a linear n -vertex 3-uniform hypergraph which does not contain a b -bounded even subgraph. In this paper, we show that if b ≥ 12, then for some absolute constant B , thus establishing f b ( n ) up to polylogarithmic factors. This leaves open the interesting case b = 2, which is the case of 2-regular subgraphs. We are able to show for some constants c , C > 0 that We conjecture that f 2 ( n ) = n 1 + o (1) as n → ∞.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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