Discriminant Circle Bundles over Local Models of Strebel Graphs and Boutroux Curves
Bibliographic record
Abstract
We study special “discriminant” circle bundles over two elementary moduli spaces of meromorphic quadratic differentials with real periods denoted by Q 0 ℝ (−7) and Q 0 ℝ ([−3]2). The space Q 0 ℝ (−7) is the moduli space of meromorphic quadratic differentials on the Riemann sphere with one pole of order seven with real periods; it appears naturally in the study of a neighborhood of the Witten cycle W5 in the combinatorial model based on Jenkins–Strebel quadratic differentials of Mg,n. The space Q 0 ℝ ([−3]2) is the moduli space of meromorphic quadratic differentials on the Riemann sphere with two poles of order at most three with real periods; it appears in the description of a neighborhood of Kontsevich’s boundary W1,1 of the combinatorial model. Applying the formalism of the Bergman tau function to the combinatorial model (with the goal of analytically computing cycles Poincaré dual to certain combinations of tautological classes) requires studying special sections of circle bundles over Q 0 ℝ (−7) and Q 0 ℝ ([−3]2). In the Q 0 ℝ (−7) case, a section of this circle bundle is given by the argument of the modular discriminant. We study the spaces Q 0 ℝ (−7) and Q 0 ℝ ([−3]2), also called the spaces of Boutroux curves, in detail together with the corresponding circle bundles.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 source (direct Gemma or distilled Codex), 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".