Quasi-Isometric Bounded Generation by Q-Rank-One Subgroups
Why this work is in the frame
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Bibliographic record
Abstract
We say that a subset X quasi-isometrically boundedly generates a finitely generated group if each element of a finite-index subgroup of can be written as a product = x 1 x 2 x r of a bounded number of elements of X, such that the word length of each x i is bounded by a constant times the word length of . A. Lubotzky, S. Mozes, and M.S. Raghunathan observed in 1993 that SL(n, Z) is quasi-isometrically boundedly generated by the elements of its natural SL(2, Z) subgroups. We generalize (a slightly weakened version of) this by showing that every S-arithmetic subgroup of an isotropic, almost-simple Q-group is quasi-isometrically boundedly generated by standard Q-rank-1 subgroups.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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