Long-time stability of small FPU solitary waves
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Bibliographic record
Abstract
Small-amplitude waves in the Fermi-Pasta-Ulam (FPU) lattice with weakly anharmonic interaction potentialsare described by the generalized Korteweg-de Vries (KdV) equation. Justification of the small-amplitudeapproximation is usually performed on the time scale, for which dynamics of the KdV equation is defined.We show how to extend justification analysis on longer time intervals provided dynamics of the generalized KdVequation is globally well-posed in Sobolev spaces and either the Sobolev norms are globally boundedor they grow at most polynomially. The time intervals are extended respectively by the logarithmic or double logarithmic factorsin terms of the small amplitude parameter. Controlling the approximation error on longer time intervalsallows us to deduce nonlinear metastability of small FPU solitary waves from orbital stability of the KdV solitary waves.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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