Perfect Matchings and Loose Hamilton Cycles in the Semirandom Hypergraph Model
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Bibliographic record
Abstract
ABSTRACT We study the 2‐offer semirandom 3‐uniform hypergraph model on vertices. At each step, we are presented with 2 uniformly random vertices. We choose any other vertex, thus creating a hyperedge of size 3. We show a strategy that constructs a perfect matching and another that constructs a loose Hamilton cycle, both succeeding asymptotically almost surely within steps. Both results extend to ‐uniform hypergraphs. Our methods are qualitatively different from those that have been used for semirandom graphs. Much of the analysis is done on an auxiliary graph that is a uniform ‐out subgraph of a random bipartite graph, and this tool may be useful in other contexts.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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