Safety factor for time-dependent axisymmetric flows of barotropic gas and ideal incompressible fluid
Bibliographic record
Abstract
The safety factor q(r, z, t) is proved to be a material conservation law for the time-dependent axisymmetric barotropic compressible gas flows and ideal incompressible fluid flows with constant density ρ. Infinite families of conserved quantities connected with the safety factor are derived. The existence of maximal vortex rings and vortex blobs which are frozen into the axisymmetric inviscid gas and fluid flows is demonstrated. A stratification in the space of ideal gas and fluid flows is obtained: if two axisymmetric states of the barotropic gas or fluid with constant density ρ are dynamically connected, then their total numbers of vortex rings must be equal (the same for the total numbers of vortex blobs) and the infinitely many corresponding conserved quantities must coincide.
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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) | 0.000 | 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".