On the circuits of splitting matroids representable over GF(p)
Bibliographic record
Abstract
<p>We apply the splitting operation defined on binary matroids (Raghunathan et al., 1998) to <span class="math inline">\(p\)</span>- matroids, where <span class="math inline">\(p\)</span>-matroids refer to matroids representable over <span class="math inline">\(GF(p).\)</span> We also characterize circuits, bases, and independent sets of the resulting matroid. Sufficient conditions to yield Eulerian <span class="math inline">\(p\)</span>-matroids from Eulerian and non-Eulerian <span class="math inline">\(p\)</span>-matroids by applying the splitting operation are obtained. A class of connected <span class="math inline">\(p\)</span>-matroids that gives connected <span class="math inline">\(p\)</span>-matroids under the splitting operation is characterized. In Application, we characterize a class of paving <span class="math inline">\(p\)</span>-matroids, which produces paving matroids after the splitting operation.</p>
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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 | 0.001 | 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 | 0.001 | 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 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".