Singular Vortex Pairs Follow Magnetic Geodesics
Bibliographic record
Abstract
Abstract We consider pairs of point vortices having circulations $\Gamma _{1}$ and $\Gamma _{2}$ and confined to a two-dimensional surface $S$. In the limit of zero initial separation $\varepsilon $, we prove that they follow a magnetic geodesic in unison, if properly renormalized. Specifically, the “singular vortex pair” moves as a single-charged particle on the surface with a charge of order $1/\varepsilon ^{2}$ in an magnetic field $B$ that is everywhere normal to the surface and of strength $|B|=\Gamma _{1} +\Gamma _{2}$. In the case $\Gamma _{1}=-\Gamma _{2}$, this gives another proof of Kimura’s conjecture [11] that singular dipoles follow geodesics.
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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 | 0.001 | 0.001 |
| 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 | 0.001 | 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".