An invariant of minimal flows coming from the $K_0$-group of a crossed product $C^*$-algebra
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Bibliographic record
Abstract
Let $M$ be a two-sided surface of genus $g>1$. In 1936 A. Weil singled out the problem of generalization of the Poincarè rotation numbers to the minimal flows $\phi$ on $M$. In this paper we suggest a solution to this problem by constructing the rotation numbers which we call Artin's. These numbers are invariants of the $K_0$-group of a crossed product $C^*$-algebra $C(X)\rtimes_{\phi}\Z$. It is shown that the dynamics of $\phi$ is completely subordinate to diophantine properties of the Artin numbers.
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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 | 0.002 | 0.001 |
| 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