Some relations between symmetries of nonlocally related systems
Bibliographic record
Abstract
The paper is concerned with relations between local symmetries of systems of partial differential equations (PDE) within trees of nonlocally related PDE systems. It is shown that potential systems arising from a given system through linearly independent conservation laws are nonlocally related to each other. Further, a theorem is proven stating that for a PDE system which has precisely n linearly independent local conservation laws, any local symmetry of the PDE system is a projection of some local symmetry of the n-plet potential system. Moreover, a criterion is presented to determine whether or not a specific local symmetry of a given PDE system is a projection of some local symmetry of a specific potential system. Examples are considered. Finally, a formula for a symmetry of a given PDE system in terms of a local symmetry of a nonlocally related subsystem is given. The formula can be used to determine whether a symmetry of the subsystem yields a local or a nonlocal symmetry of the given system, without the need to undertake a full symmetry classification and comparison between the given system and the subsystem.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".