Higher length-twist coordinates, generalized Heun's opers, and twisted\n superpotentials
Bibliographic record
Abstract
In this paper we study a proposal of Nekrasov, Rosly and Shatashvili that\ndescribes the effective twisted superpotential obtained from a class S theory\ngeometrically as a generating function in terms of certain complexified\nlength-twist coordinates, and extend it to higher rank. First, we introduce a\nhigher rank analogue of Fenchel-Nielsen type spectral networks in terms of a\ngeneralized Strebel condition. We find new systems of spectral coordinates\nthrough the abelianization method and argue that they are higher rank analogues\nof the Nekrasov-Rosly-Shatashvili Darboux coordinates. Second, we give an\nexplicit parametrization of the locus of opers and determine the generating\nfunctions of this Lagrangian subvariety in terms of the higher rank Darboux\ncoordinates in some specific examples. We find that the generating functions\nindeed agree with the known effective twisted superpotentials. Last, we relate\nthe approach of Nekrasov, Rosly and Shatashvili to the approach using quantum\nperiods via the exact WKB method.\n
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".