A Shimura–Shintani correspondence for rigid analytic cocycles of higher weight
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Bibliographic record
Abstract
Abstract This paper takes the first steps towards a systematic study of additive rigid meromorphic cocycles of higher weight. These were introduced by Darmon and Vonk, who focused on additive cocycles of weight two and their multiplicative lifts. After classifying certain rigid meromorphic cocycles of weight <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mn>2</m:mn> <m:mo></m:mo> <m:mi>k</m:mi> </m:mrow> </m:math> {2k} , we construct an explicit holomorphic kernel function realizing a Shimura–Shintani style correspondence from modular forms of weight <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>k</m:mi> <m:mo>+</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>/</m:mo> <m:mn>2</m:mn> </m:mrow> </m:mrow> </m:math> {k+1/2} and level <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mn>4</m:mn> <m:mo></m:mo> <m:msup> <m:mi>p</m:mi> <m:mn>2</m:mn> </m:msup> </m:mrow> </m:math> {4p^{2}} to rigid analytic cocycles of weight <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mn>2</m:mn> <m:mo></m:mo> <m:mi>k</m:mi> </m:mrow> </m:math> {2k} on <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>SL</m:mi> <m:mn>2</m:mn> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mi>ℤ</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">[</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>/</m:mo> <m:mi>p</m:mi> </m:mrow> <m:mo stretchy="false">]</m:mo> </m:mrow> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {\operatorname{SL}_{2}(\mathbb{Z}[1/p])} .
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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