Motivic Proof of a Character Formula for SL(2)
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Bibliographic record
Abstract
This paper provides a proof of a p-adic character formula by means of motivic integration. We use motivic integration to produce virtual Chow motives that control the values of the characters of all depth-zero supercuspidal representations on all topologically unipotent elements of p-adic SL(2); likewise, we find motives for the values of the Fourier transform of all regular elliptic orbital integrals having minimal nonnegative depth in their own Cartan subalgebra, on all topologically nilpotent elements of p-adic sl(2). We then find identities in the ring of virtual Chow motives over ℚ that relate these two classes of motives. These identities provide explicit expressions for the values of characters of all depth-zero supercuspidal representations of p-adic SL(2) as linear combinations of Fourier transforms of semisimple orbital integrals, thus providing a proof of a p-adic character formula.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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