The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equation
Bibliographic record
Abstract
In this paper we study the confluence of two regular singular points of the hypergeometric equation into an irregular one. We study the consequence of the divergence of solutions at the irregular singular point for the unfolded system. Our study covers a full neighborhood of the origin in the confluence parameter space. In particular, we show how the divergence of solutions at the irregular singular point explains the presence of logarithmic terms in the solutions at a regular singular point of the unfolded system. For this study, we consider values of the confluence parameter taken in two sectors covering the complex plane. In each sector, we study the monodromy of a first integral of a Riccati system related to the hypergeometric equation. Then, on each sector, we include the presence of logarithmic terms into a continuous phenomenon and view a Stokes multiplier related to a 1-summable solution as the limit of an obstruction that prevents a pair of eigenvectors of the monodromy operators, one at each singular point, to coincide.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".