Bibliographic record
Abstract
In 1904, lie Cartan developed a new structure theory for Lie pseudo-groups based on his theory of exterior differential systems (Sur la structure des groupes infinis de transformations, in: Oeuvres Complte, Part.II, vol. 2. Gauthier-Villars, Paris, 1953, 571-714).About a century later, in 2005, Olver and Pohjanpelto proposed a new approach to derive the structure equations of Lie pseudo-groups (Maurer-Cartan equations and structure of Lie pseudo-groups, Selecta Math.11 (2005) 99-126).The two theories are compared and it is shown that for intransitive Lie pseudo-groups they do not agree.To make the two theories compatible, we show that Cartan's structure equations must be restricted to the orbits of the pseudo-group action.The repercussion of this modification on Cartan's concept of essential invariants is discussed.Also, the infinitesimal interpretation of Cartan's structure equations for transitive Lie pseudo-groups, given in 1965 by Singer and Sternberg (The infinite groups of Lie and Cartan I: The transitive groups, J. d'Analyse Math.15 (1965), 1-115).is extended to intransitive Lie pseudo-groups.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".