Why this work is in the frame
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Bibliographic record
Abstract
Practically every book on the Inverse Scattering Transform method for solving the Cauchy problem for KdV and other integrable systems refers to this method as nonlinear Fourier Transform. If it is indeed so, the method should lead to a nonlinear analogue of the Fourier expansion formula $u(t,x)=\int\limits_{-\infty}^{+\infty} \hat{u}(k) e^{i\big(kx-\omega(k)t\big)} dk.$ In this paper a special class of solutions of KdV whose role is similar to that of $e^{i\big(kx-\omega(k)t\big)}$ is discussed. Theory of these solutions, referred to here as harmonic breathers, is developed and it is shown that these solutions may be used to construct more general solutions of KdV similarly to how the functions $e^{i\big(kx-\omega(t)\big)} $ are used to perform the same task in the theory of Fourier transform. Nonlinear superposition formula for general solutions of KdV similar to the Fourier expansion formula is conjectured.
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