The dimer model on Riemann surfaces, I
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Bibliographic record
Abstract
This is the first article in a series of two papers in which we study the\nTemperleyan dimer model on an arbitrary bounded Riemann surface of finite\ntopolgical type. The end goal of both papers is to prove the convergence of\nheight fluctuations to a universal and conformally invariant scaling limit. In\nthis part we show that the dimer model on the Temperleyan superposition of a\ngraph embedded on the surface and its dual is well posed, provided that we\nremove an appropriate number of punctures. We further show that the resulting\ndimer configuration is in bijection with an object which we call Temperleyan\nforest, whose law is characterised in terms of a certain topological condition.\nFinally we discuss the relation between height differences and Temperleyan\nforest, and give a criterion guaranteeing the convergence of the height\nfluctuations in terms of the Temperleyan forest.\n
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.003 |
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