Bibliographic record
Abstract
In this paper, we explore the modular differential equation [Formula: see text] on the upper half-plane [Formula: see text], where F is a weight 4 modular form for [Formula: see text]. Our approach centers on solving the associated Schwarzian equation [Formula: see text], where [Formula: see text] represents the Schwarzian derivative of a meromorphic function h on [Formula: see text]. We derive conditions under which the solutions to this equation are modular functions for subgroups of the modular group and provide explicit expressions for these solutions in terms of classical modular functions. Key tools in our analysis include the theory of equivariant functions on the upper half-plane and the representation theory of level 2 subgroups of the modular group. The corresponding case where F is a modular form for the full modular group [Formula: see text] has been previously addressed in previous work by the second author.
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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 | 0.004 |
| 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) | 0.011 | 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".