Bibliographic record
Abstract
This text is an exposition of non-Archimedean curves and Schottky\nuniformization from the point of view of Berkovich geometry. It consists of two\nparts, the first one of an introductory nature, and the second one more\nadvanced. The first part is meant to be an introduction to the theory of\nBerkovich spaces focused on the case of the affine line. We define the\nBerkovich affine line and present its main properties, with many details:\nclassification of points, path-connectedness, metric structure, variation of\nrational functions, etc. Contrary to many other introductory texts, we do not\nassume that the base field is algebraically closed. The second part is devoted\nto the theory of Mumford curves and Schottky uniformization. We start by\nbriefly reviewing the theory of Berkovich curves, then introduce Mumford curves\nin a purely analytic way (without using formal geometry). We define Schottky\ngroups acting on the Berkovich projective line, highlighting how geometry and\ngroup theory come together to prove that the quotient by the action of a\nSchottky group is an analytic Mumford curve. Finally, we present an analytic\nproof of Schottky uniformization, showing that any analytic Mumford curves can\nbe described as a quotient of this kind. The guiding principle of our\nexposition is to stress notions and fully prove results in the theory of\nnon-Archimedean curves that, to our knowledge, are not fully treated in other\ntexts.\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) | 0.000 | 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 | 0.003 |
| Research integrity | 0.000 | 0.000 |
| 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".