Bibliographic record
Abstract
We establish existence theorems for the image of the normalized character map of the p -adic Heisenberg algebra S taking values in the algebra of Serre p -adic modular forms M p . In particular, we describe the construction of an analytic family of states in S whose character values are the well-known Λ-adic family of p -adic Eisenstein series of level one built from classical Eisenstein series. This extends previous work treating a specialization at weight 2, and illustrates that the image of the character map contains nonzero p -adic modular forms of every p -adic weight. In a different direction, we prove that for p = 2 the image of the rescaled character map contains every overconvergent 2-adic modular form of weight zero and tame level one; in particular, it contains the polynomial algebra Q 2 [ j − 1 ] . For general primes p , we study the square-bracket formalism for S and develop the idea that although states in S do not generally have a conformal weight, they can acquire a p -adic weight in the sense of Serre.
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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".