Nonlinear stability of self-gravitating massive fields. A wave-Klein–Gordon model
Why this work is in the frame
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Bibliographic record
Abstract
Abstract In recent years, significant progress has been made in understanding the global evolution of self-gravitating massive matter in the small-perturbative regime near Minkowski spacetime. To investigate the interaction between a Klein–Gordon equation and Einstein’s field equations, we developed a new approach called the Euclidean-hyperboloidal foliation method. This method involves constructing a spacetime foliation that is well-suited for deriving precise decay estimates for wave and Klein–Gordon equations in curved spacetime. In this article, we provide an overview of our method and present a complete proof for a wave-Klein–Gordon model that captures some of the key challenges associated with the Einstein-matter system.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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