Solitary Waves and Dynamics for Subcritical Perturbations of Energy\n Critical NLS
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We consider a perturbed energy critical focusing Nonlinear Schr\\"odinger\nEquation in three dimensions. We construct solitary wave solutions for focusing\nsubcritical perturbations as well as defocusing supercritical perturbations.\nThe construction relies on the resolvent expansion, which is singular due to\nthe presence of a resonance. Specializing to pure power focusing subcritical\nperturbations we demonstrate, via variational arguments, and for a certain\nrange of powers, the existence of a ground state solitary wave, which is then\nshown to be the previously constructed solution. Finally, we present a\ndynamical theorem which characterizes the fate of radially-symmetric solutions\nwhose initial data are below the action of the ground state. Such solutions\nwill either scatter or blow-up in finite time depending on the sign of a\ncertain function of their initial data.\n
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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.002 |
| 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