Noncommutative Chern-Weil theory and the combinatorics of wheeling
Why this work is in the frame
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Bibliographic record
Abstract
This work applies the ideas of Alekseev and Meinrenken's noncommutative Chern-Weil theory to describe a completely combinatorial and constructive proof of the wheeling theorem. In this theory, the crux of the proof is, essentially, the familiar demonstration that a characteristic class does not depend on the choice of connection made to construct it. To a large extent, this work may be viewed as an exposition of the details of some of Alekseev and Meinrenken's theory written for Kontsevich integral specialists. Our goal was a presentation with full combinatorial detail in the setting of Jacobi diagrams. To achieve this goal, certain key algebraic steps required replacement with substantially different combinatorial arguments.
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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 | 0.004 | 0.004 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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