Local properties of the random Delaunay triangulation model and topological models of 2D gravity
Why this work is in the frame
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Bibliographic record
Abstract
Delaunay triangulations provide a bijection between a set of N+3 points in generic position in the complex plane, and the set of triangulations with given circumcircle intersection angles. The uniform Lebesgue measure on these angles translates into a Kähler measure for Delaunay triangulations, or equivalently on the moduli space \mathcal M_{0,N+3} of genus zero Riemann surfaces with N+3 marked points. We study the properties of this measure. First we relate it to the topological Weil–Petersson symplectic form on the moduli space \mathcal M_{0,N+3} . Then we show that this measure, properly extended to the space of all triangulations on the plane, has maximality properties for Delaunay triangulations. Finally we show, using new local inequalities on the measures, that the volume \mathcal{V}_N on triangulations with N+3 points is monotonically increasing when a point is added, N\to N+1 . We expect that this can be a step towards seeing that the large N limit of random triangulations can tend to the Liouville conformal field theory.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| 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