Tree-tubings and the combinatorics of resurgent Dyson–Schwinger equations
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Bibliographic record
Abstract
We give a novel combinatorial interpretation for the perturbative series solutions to a class of Dyson–Schwinger equations. We show how binary tubings of rooted trees with labels from an alphabet on the tubes, and where the labels satisfy certain compatibility constraints, can be used to give series solutions to Dyson–Schwinger equations with a single Mellin transform which is the reciprocal of a polynomial with rational roots in a fully combinatorial way. Further, the structure of these tubings leads directly to systems of differential equations for the anomalous dimension that are ideally suited for resurgent analysis. We give a general result in the distinct root case and investigate the effect of repeated roots, which drastically changes the asymptotics and the transseries structure.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 it