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Record W4412071566 · doi:10.1016/j.jnt.2025.05.017

On p-adic modularity in the p-adic Heisenberg algebra

2025· article· en· W4412071566 on OpenAlexafffund
Cameron Franc, Geoffrey Mason

Bibliographic record

VenueJournal of Number Theory · 2025
Typearticle
Languageen
FieldMathematics
TopicAdvanced Algebra and Geometry
Canadian institutionsMcMaster University
FundersNatural Sciences and Engineering Research Council of CanadaSimons Foundation
KeywordsMathematicsModularity (biology)Algebra over a fieldPure mathematicsHeisenberg group

Abstract

fetched live from OpenAlex

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.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.002
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.046
Threshold uncertainty score0.902

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0010.000

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.

Opus teacher head0.018
GPT teacher head0.339
Teacher spread0.320 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one teacher head, not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations1
Published2025
Admission routes2
Has abstractyes

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