Symmetry classification of systems of differential-difference equations
Bibliographic record
Abstract
The Lie point symmetries of a coupled system of two nonlinear differential-difference equations are investigated. The equations arise from a model describing the interaction of two long molecular chains. We have classified all symmetry algebras containing an sl(2,R) subalgebra. Examples are given for which the symmetry algebra is 10-dimensional and infinite-dimensional. Resume Nous etudions les symetries d’un systeme de deux equations differentielles aux differences. Ces equations proviennent d’un modele pouvant decrire l’interaction de deux longues châines moleculaires. Nous avons classifie toutes les algebres de symetrie contenant une certaine representation de sl(2,R) comme sous-algebre. Nous donnons des exemples pour lesquels l’algebre de symetrie est de dimension 10 ou de dimension infinie.
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How this classification was reachedexpand
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 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".