Bibliographic record
Abstract
In this paper we study the stability of equilibrium configurations for two-dimensional smooth convex bodies in the absence of gravity, focusing on one example in particular, the ellipse. We also begin to consider the floating configurations of bodies which are not strictly convex; that is, bodies that have one or more linear sides. We will show that a body cannot float in a stable equilibrium with the fluid interface intersecting the interior of a straight side in a single point, and then using this result we will proceed to study the stability of convex bodies comprised of only straight sides consequently deriving a necessary and sufficient condition for stable equilibrium of polygonal bodies. We illustrate our findings using the square as an example. Finally, we prove several results concerning the number of stable and unstable configurations for an n-sided regular polygon (n≥3) including a result guaranteeing the existence of a stable global energy minimum provided the contact angle γ is not 0 or π.
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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".