Polynomiality of the faithful dimension for nilpotent groups over finite truncated valuation rings
Bibliographic record
Abstract
Given a finite group G \mathrm {G} , the faithful dimension of G \mathrm {G} over C \mathbb {C} , denoted by m f a i t h f u l ( G ) m_\mathrm {faithful}(\mathrm {G}) , is the smallest integer n n such that G \mathrm {G} can be embedded in G L n ( C ) \mathrm {GL}_n(\mathbb {C}) . Continuing the work initiated by Bardestani et al. [Compos. Math. 155 (2019), pp. 1618–1654], we address the problem of determining the faithful dimension of a finite p p -group of the form G R ≔ exp ( g R ) \mathscr {G}_R≔\exp (\mathfrak {g}_R) associated to g R ≔ g ⊗ Z R \mathfrak {g}_R≔\mathfrak {g}\otimes _\mathb
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
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 source (direct Gemma or distilled Codex), 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".