Efficient enumeration of rooted maps of a given orientable genus by number of faces and vertices
Bibliographic record
Abstract
We simplify the recurrence satisfied by the polynomial part of the generating function that counts rooted maps of positive orientable genus <em&gtg</em&gt by number of vertices and faces. We have written an optimized program in C++ for computing this generating function and constructing tables of numbers of rooted maps, and we describe some of these optimizations here. Using this program we extended the enumeration of rooted maps of orientable genus <em&gtg</em&gt by number of vertices and faces to <em&gtg</em&gt = 4, 5 and 6 and by number of edges to <em&gtg</em&gt = 5 and 6 and conjectured a further simplification of the generating function that counts rooted maps by number of edges. Our program is documented and available on request, allowing anyone with a sufficiently powerful computer to carry the calculations even further.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 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".