Sur la catégorie amassée d'une surface marquée
Bibliographic record
Abstract
We study in this thesis the cluster category C[subscript S,M] and cluster algebra A[Subscript S,M] of a marked surface (S, M) without punctures. We give a geometric characterization of the indecomposable objects in C[subscript S,M] as homotopy classes of curves in (S, M) and one-parameter families related to non-contractible closed curves in (S , M). Moreover, the Auslander-Reiten structure of the category C[Subscript S,M] is described in geometric terms and we show that the objects without self-extensions in C[Subscript S,M] correspond to curves in (S, M) without self-intersections. As a consequence, we establish that every rigid indecomposable object is reachable from an initial triangulation. As for the cluster algebra A[Subscript S,M], we give a module-theoretic interpretation of Schiffler's expansion formula defined in [42]. Based on the properties of the cluster category C[Subscript S,M], we show the coincidence of Schiffler-Thomas' expansion formula and the cluster character defined in [36].
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 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".