Bibliographic record
Abstract
In this paper, we present a method for constructing invariant solutions of the supersymmetric Chaplygin gas in (1 + 1) dimensions. This approach is based on the use of a generalized Legendre transformation, through which we transform the original field equations into a new set of equations involving the velocity and sound speed of the fluid as independent variables. We describe the Lie symmetry properties of the equations in both coordinate systems, and make use of a systematic subgroup classification to determine certain classes of group-invariant solutions of the transformed field equations. Where it is possible, the Legendre transformation is applied in reverse in order to obtain equivalent solutions of the standard field equations. A number of analytic solutions of the supersymmetric Chaplygin gas in one spatial dimension are found. In addition, certain basic elements of a possible extension of our method to the supersymmetric Chaplygin gas in two spatial dimensions have been formulated. In particular, the (2 + 1)-dimensional analogue of the transformed equation has been determined, and some of its Lie point symmetries have been identified. For a certain specific case, it has been demonstrated how an invariant solution can be inverted and then extended to a solution of the planar supersymmetric model.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.000 | 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".