Bibliographic record
Abstract
We study interaction energies given by various kernels, and investigate how these kernels drive the formation of multiple flocks within a larger population. We show that for a class of kernels having a ``well-barrier'' shape that the energy is minimized by a sequence of indicators of finitely many balls whose supports move further and further apart. The dichotomy case of the concentration compactness principle is a key ingredient in our proof. To better understand the underlying geometry and the role of the height and width of the repulsive barrier, we also consider a toy model which forbids points in the support of an admissible density from being within a certain range of distances from one another. We show in one dimensions, that no matter the width of this range the energy is minimized by the indicator of a union of well separated intervals of equal length and one smaller interval, however other minimizers are possible. Finally, we also consider weakly repulsive kernels and show that Wasserstein $d_{\infty}$ local minimizers must saturate the density constraint.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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 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".