∗Departement de Mathematiques et de Statistiques, Universite de Montreal
Bibliographic record
Abstract
Planar quadratic vector fields possessing at least five straight lines as particular integrals (in-cluding the line at infinity and their multiplicities) are acted upon by the affine group of transformations and time rescalings. In this article we characterize in terms of algebraic invariants and comitants and geometrically, using divisors of the complex projective plane and on the line at infinity, this class of differential systems. We list a system of representatives of all orbits of this family under the group action. Résumé Le groupe des transformations affines et des changements d’echelle du temps agit sur les champs de vecteurs quadratiques ayant au moins cinq intégrales particulières qui sont des droites (la droite a ̀ l’infini ainsi que les éventuelles multiplicités comprises). Dans ce travail nous caractérisons en terms d’invariants et de comitants algébriques, aussi géométriqement en utilisant des diviseurs sur le plan projectif complexe et sur la droite a l’infini, cette classe de systèmes différentielles. Nous donnons un système de représentants des orbites par rapport a ̀ cette action de groupe. 1
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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.004 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.153 | 0.022 |
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".