Lattices of Neumann oscillators and Maxwell–Bloch equations
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Bibliographic record
Abstract
Accepted for publication in Nonlinearity We introduce a family of new non-linear many-body dynamical systems which we call the Neumann lattices. These are lattices of N interacting Neu-mann oscillators. The interactions are of magnetic type. We construct large families of conserved quantities for the Neumann lattices. For this purpose we develop a new method of constructing the first integrals which we call the reduced curvature condition. Certain Neumann lattices are natural partial discretizations of the Maxwell-Bloch equations. The Maxwell-Bloch equations have a natural Hamiltonian structure whose discretizations yields a twisted Poisson structures (in the sense of P. Ševera and A. Weinstein) for the Neu-mann lattices. Thus the Neumann lattices are candidates for integrable systems with twisted Poisson structures. 1
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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) | 0.000 | 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