Bibliographic record
Abstract
Abstract. Suppose that X and Y are surfaces of finite topologi-cal type, where X has genus g ≥ 6 and Y has genus at most 2g−1; in addition, suppose that Y is not closed if it has genus 2g − 1. Our main result asserts that every non-trivial homomorphism Map(X) → Map(Y) is induced by an embedding, i.e. a combina-tion of forgetting punctures, deleting boundary components and subsurface embeddings. In particular, if X has no boundary then every non-trivial endomorphism Map(X) → Map(X) is in fact an isomorphism. As an application of our main theorem we obtain that, under the same hypotheses on genus, if X and Y have finite analytic type then every non-constant holomorphic map M(X) → M(Y) between the corresponding moduli spaces is a forgetful map. In particular, there are no such holomorphic maps unless X and Y have the same genus and Y has at most as many marked points as X. A nuestras madres, cada uno a la suya. 1.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".