Spherical Space Forms: Homotopy Types and Self-Equivalences for the Group (ℤ/<i>a</i> ⋊ ℤ/<i>b</i>) × <i>SL</i><sub>2</sub> (<i><sub>p</sub></i>)
Bibliographic record
Abstract
Abstract Let G = (ℤ/ a ⋊ ℤ/ b ) × SL 2 ( p ), and let X ( n ) be an n -dimensional CW -complex of the homotopy type of an n -sphere. We study the automorphism group Aut( G ) in order to compute the number of distinct homotopy types of spherical space forms with respect to free and cellular G -actions on all CW -complexes X (2 dn − 1), where 2 d is the period of G . The groups ε( X (2 dn − 1)/ μ ) of self homotopy equivalences of space forms X (2 dn − 1)/ μ associated with free and cellular G -actions μ on X (2 dn − 1) are determined as well.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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".