Minimal H_3 actions and simple quotients of discrete 7-dimensional nilpotent groups
Why this work is in the frame
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Bibliographic record
Abstract
For connected nilpotent groups, 7 is the lowest dimension where there are infinitely many non-isomorphic groups, and also where some groups have no discrete cocompact subgroups. Here one infinite family of 7-dimensional connected groups is studied, discrete cocompact subgroups H are found for some of them, and then the faithful simple quotients A of $C^{*}(\roman H)$ are identified. Such A are shown to be isomorphic to $C^{*}$-crossed products $C^{*}(\roman H_ 3,\Cal C(\Bbb T^3))$ generated by some intriguing effective minimal distal flows $(\roman H_3,\Bbb T^ 3)$, where $\roman H_3$ is the discrete 3-dimensional Heisenberg group.
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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 | 0.000 | 0.001 |
| 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) | 0.004 | 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