Why this work is in the frame
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Bibliographic record
Abstract
The quasi-homogeneous two-body problem aims at studying the interaction between two point particles under a prescribed potential in the form of W(r)=−Ara−Brb, where A, B > 0 are constants and r is the mutual distance between two particles. Important examples include the Manev potential (a = 1, b = 2) and the Schwarzschild potential (a = 1, b = 3). It is well known that power two serves as a threshold value for the homogeneous potential: One is able to observe significant differences regarding the solution dynamics as the power of the homogeneous potential exceeds two from below. This phenomenon remains observable for quasi-homogeneous potentials. In this paper, we shall provide a complete characterization of the whole phase space of the quasi-homogeneous two-body problem in terms of global existence and singularity for all the possible b > a > 0. In particular, one is able to generalize the result of the Manev and Schwarzschild two-body problem to all the quasi-homogeneous potentials. Two techniques are presented in this paper: One is the variational method based on the energy, and the other is a direct computation of collision time based on the integrability of two-body systems.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 it