Formal composition of hybrid systems
Bibliographic record
Abstract
We develop a compositional framework for formal synthesis of hybrid systems using the language of category theory.More specifically, we provide mutually compatible tools for hierarchical, sequential, and independent parallel composition.In our framework, hierarchies of hybrid systems correspond to template-anchor pairs, which we model as spans of subdividing and embedding semiconjugacies.Hierarchical composition of template-anchor pairs corresponds to the composition of spans via fiber product.To model sequential composition, we introduce "directed hybrid systems," each of which flows from an initial subsystem to a final subsystem in a Conley-theoretic sense.Sequential composition of directed systems is given by a pushout of graph embeddings, rewriting the continuous dynamics of the overlapping subsystem to prioritize the second directed system.Independent parallel composition corresponds to a categorical product with respect to semiconjugacy.To formalize the compatibility of these three types of composition, we construct a vertically cartesian double category of hybrid systems where the vertical morphisms are semiconjugacies, and the horizontal morphisms are directed hybrid systems.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".