On the rationality of period integrals and special value formulas in the compact case
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Bibliographic record
Abstract
We study rationality properties of period integrals that appear in the Gan–Gross–Prasad conjectures in the compact case using Gross’ theory of algebraic modular forms. In situations where the refined Gan–Gross–Prasad are known, our rationality result for period can be interpreted as a special value formula for automorphic L -functions which proves automorphic versions of Deligne’s conjecture on rationality of periods. Moreover, this special value formula is well suited to p -adic interpolation, as illustrated in [10].
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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