Representation zeta function of a family of maximal class groups: Non-exceptional primes
Bibliographic record
Abstract
Abstract We use a constructive method to obtain all but finitely many 𝑝-local representation zeta functions of a family of finitely generated nilpotent groups <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>M</m:mi> <m:mi>n</m:mi> </m:msub> </m:math> M_{n} with maximal nilpotency class. For representation dimensions coprime to all primes <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>p</m:mi> <m:mo><</m:mo> <m:mi>n</m:mi> </m:mrow> </m:math> p<n , we construct all irreducible representations of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>M</m:mi> <m:mi>n</m:mi> </m:msub> </m:math> M_{n} by defining a standard form for the matrices of these representations.
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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 | 0.000 |
| 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 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".