Why this work is in the frame
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Bibliographic record
Abstract
In this paper we study spiderweb central configurations for the N-body problem, i.e configurations given by $$N=n \times \ell +1$$ masses located at the intersection points of $$\ell $$ concurrent equidistributed half-lines with n circles and a central mass $$m_0$$ , under the hypothesis that the $$\ell $$ masses on the i-th circle are equal to a positive constant $$m_i$$ ; we allow the particular case $$m_0=0$$ . We focus on constructive proofs of the existence of spiderweb central configurations, which allow numerical implementations. Additionally, we prove by a rigorous numerical method the uniqueness of such central configurations when $$\ell \in \{2,\ldots ,9\}$$ and arbitrary n and $$m_i$$ ; under the constraint $$m_1\ge m_2\ge \cdots \ge m_n$$ we also prove uniqueness for $$\ell \in \{10,\ldots ,18\}$$ and n not too large. We also give an algorithm providing a rigorous proof of the existence and local unicity of such central configurations when given as input a choice of n, $$\ell $$ and $$m_0, \ldots ,m_n$$ . Finally, our numerical simulations highlight some interesting properties of the mass distribution.
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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 | 0.000 |
| 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 it