Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields
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Bibliographic record
Abstract
Let F be a non-Archimedean local field with the ring of integers \mathcal{O} and the prime ideal \mathfrak{p} and let G=\mathbf G_{\mathrm {ad}} (\mathcal O/\mathfrak p^n) be the adjoint Chevalley group. Let m_{\sf f} (G) denote the smallest possible dimension of a faithful representation of G . Using the Stone–von Neumann theorem, we determine a lower bound for m_{\sf f} (G) which is asymptotically the same as the results of Landazuri, Seitz and Zalesskii for split Chevalley groups over \mathbb F_q . Our result yields a conceptual explanation of the exponents that appear in the aforementioned results.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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