Spontaneous periodic orbits in the Navier-Stokes flow
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Bibliographic record
Abstract
In this paper, a general method to obtain constructive proofs of existence of\nperiodic orbits in the forced autonomous Navier-Stokes equations on the\nthree-torus is proposed. After introducing a zero finding problem posed on a\nBanach space of geometrically decaying Fourier coefficients, a\nNewton-Kantorovich theorem is applied to obtain the (computer-assisted) proofs\nof existence. The required analytic estimates to verify the contractibility of\nthe operator are presented in full generality and symmetries from the model are\nused to reduce the size of the problem to be solved. As applications, we\npresent proofs of existence of spontaneous periodic orbits in the Navier-Stokes\nequations with Taylor-Green forcing.\n
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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 | 0.000 | 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) | 0.001 | 0.001 |
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