Reduced systems of (2, 2) pseudo-Euclidean noncommutative self-dual Yang$ndash$Mills theories
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Bibliographic record
Abstract
Self-dual Yang–Mills equations on noncommutative spaces associated with pseudo-Euclidean space of signature (2, 2) are shown to be related via dimensional reductions to noncommutative formulations of Toda equations, of generalized nonlinear Schrödinger (NS) equations, of the super-Korteweg–de Vries (super-KdV) as well as of the matrix KdV equations. The noncommutative extensions of their linear systems and bicomplexes associated with conserved quantities are discussed as well. A q-plane version of the KdV equation with linear system is also shown.
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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) | 0.001 | 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