Equivariant bundles and isotropy representations
Why this work is in the frame
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Bibliographic record
Abstract
We introduce a new construction, the isotropy groupoid , to organize the orbit data for split Γ-spaces. We show that equivariant principal G-bundles over split Γ-CW complexes X can be effectively classified by means of representations of their isotropy groupoids. For instance, if the quotient complex A = Γ \ X is a graph, with all edge stabilizers toral subgroups of Γ, we obtain a purely combinatorial classification of bundles with structural group G a compact connected Lie group. If G is abelian, our approach gives combinatorial and geometric descriptions of some results of Lashof–May–Segal [18] and Goresky–Kottwitz–MacPherson [10].
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 |
| Research integrity | 0.001 | 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