Topological characteristics of random triangulated surfaces
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Bibliographic record
Abstract
Abstract We consider the topological characteristics of orientable surfaces generated by randomly gluing n triangles together. Our results are most conveniently expressed in terms of a parameter h = n / 2 + χ, where χ is the Euler characteristic of the surface. Simulations and results for similar models suggest that Ex [ h ] = log(3 n ) + γ + o (1) and Var [ h ] = log(3 n ) + γ ‐ π 2 / 6 + o (1). We prove that Ex [ h ] = log n + O (1) and Var [ h ] = O (log n ). We also derive results concerning a number of other topological invariants and combinatorial characteristics of these random surfaces. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006
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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 | 0.000 | 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) | 0.001 | 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