An example of rapid evolution of complex limit cycles
Why this work is in the frame
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Bibliographic record
Abstract
In the current article we study complex cycles of highermultiplicity in a specific polynomial family of holomorphicfoliations in the complex plane. The family in question is aperturbation of an exact polynomial one-form giving rise to afoliation by Riemann surfaces. In this setting, a complex cycle isdefined as a nontrivial element of the fundamental group of a leaffrom the foliation. In addition to that, we introduce the notionof a multi-fold cycle and show that in our example there exists alimit cycle of any multiplicity. Furthermore, such a cycle givesrise to a one-parameter family of cycles continuously depending onthe perturbation parameter. As the parameter decreases in absolutevalue, the cycles from the continuous family escape from a verylarge subdomain of the complex plane.
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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) | 0.002 | 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