Bibliographic record
Abstract
Let R be a finitely generated virtually free group (a finite extension of a free group) and let H be a finitely generated subgroup of R . Denote by \hat R the profinite completion of R and let \bar H be the closure of H in \hat R . It is proved that the normalizer N_{\hat R}(\bar H) of \bar H in \hat R is the closure in \hat R of N_{R}(H) . The proof is based on the fact that R is the fundamental group of a graph of finite groups over a finite graph and on the study of the minimal H -invariant subtrees of the universal covering graph of that graph of groups. As a consequence we prove results of the following type: let R be a group that is an extension of a free group by finite solvable group, and let x,y\in R ; then x and y are conjugate in R if their images are conjugate in every finite quotient of R .
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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".