Bibliographic record
Abstract
This paper is an outgrowth of the results in the domain of rolling obtained in our recent paper written with F. Silva Leite and I. Markina, and the earlier papers on the rollings of spheres produced with J. Zimmerman. We show that the rolling equations associated with a symmetric semi-Riemannian manifold rolling on its tangent space at a fixed point on the manifold essentially have the same structure as the rolling equations for the n-dimensional sphere rolling on the horizontal hyperplane; that is, we show that the rolling equations are described by a left-invariant distribution D on a Lie group G with the Lie bracket growth D + [D,D] + [D, [D,D]] = TG, reminiscent of the growth (2, 3, 5) for the two spheres rolling on the horizontal plane. We then define rolling geodesics on semi-Riemannian spaces as extensions of sub-Riemannian geodesics in the Riemannian symmetric spaces, and show that the rolling geodesics are the projections of the extremal curves, which, remarkably, are the solution curves of a completely integrable Hamiltonian system in the cotangent bundle of the configuration space. Finally, we illustrate the theory with a few noteworthy examples.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), 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".