Bibliographic record
Abstract
Abstract Carvalho, Lucchesi and Murty (2006, How to build a brick, Discrete Math., 306, 2383‐2410) gave a generation procedure for bricks. In particular, they showed that every brick may be constructed from , the triangular prism , and the Petersen graph. The object of this paper is to establish a generation procedure that is specific to the class of near‐bipartite bricks. In particular, we show that every near‐bipartite brick may be constructed from and so that each intermediate brick is also near‐bipartite. Norine and Thomas (2007, Generating bricks, J. Combin. Theory Ser. B, 97, 769‐817) proved a generation theorem for simple bricks. In a subsequent work with Marcelo H. de Carvalho (2017, Generating simple near‐bipartite bricks, https://arxiv.org/abs/1704.08796 ), we use the results of this paper to prove a generation theorem for simple near‐bipartite bricks.
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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 | 0.006 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.000 | 0.002 |
| 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".