Epsilon controllability of nonlinear systems on polytopes
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Bibliographic record
Abstract
The paper introduces the notion of epsilon controllability of nonlinear systems on polytopes, and then uses it to approximately solve the mutual accessibility problems of nonlinear systems on polytopes. In particular, we first show that if one constructs a polytopic cover of a given polytope such that the affine system resulting from the linearization of the nonlinear system inside each polytopic region of the cover is in-block controllable, then starting from any initial state in the interior of the given polytope, one can steer the nonlinear system to an epsilon neighborhood of any final state in the interior of the polytope in finite time, where epsilon depends on the size of the polytopic regions of the cover. We then study a hierarchy of covers, representing the nonlinear system at different levels of accuracy, and provide a constructive algorithm for achieving approximate mutual accessibility of nonlinear systems on polytopes.
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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