Overconvergent Eichler–Shimura isomorphisms
Why this work is in the frame
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Bibliographic record
Abstract
Abstract Given a prime $p\gt 2$ , an integer $h\geq 0$ , and a wide open disk $U$ in the weight space $ \mathcal{W} $ of ${\mathbf{GL} }_{2} $ , we construct a Hecke–Galois-equivariant morphism ${ \Psi }_{U}^{(h)} $ from the space of analytic families of overconvergent modular symbols over $U$ with bounded slope $\leq h$ , to the corresponding space of analytic families of overconvergent modular forms, all with ${ \mathbb{C} }_{p} $ -coefficients. We show that there is a finite subset $Z$ of $U$ for which this morphism induces a $p$ -adic analytic family of isomorphisms relating overconvergent modular symbols of weight $k$ and slope $\leq h$ to overconvergent modular forms of weight $k+ 2$ and slope $\leq h$ .
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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 | 0.003 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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 | 0.000 | 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 it