Equivalence to dissipative Hamiltonian realization
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Bibliographic record
Abstract
This paper considers the problem of deriving a generalized Hamiltonian potential for autonomous dynamical systems. For a given vector field, the objective is to construct a locally defined dissipative Hamiltonian generating function for the system. The proposed approach consists of studying the deviation of the given vector field from a canonically defined Hamiltonian vector field. First, we obtain a one-form by taking the interior product of a nonvanishing two-form with respect to the vector field. We then construct a homotopy operator on a star-shaped region that decomposes the system into an exact part and an anti-exact one. Equivalence between the exact part and an exact one-form generated from a known potential is then used to compute the locally defined dissipative potential of the original system. An example is presented to illustrate the method.
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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