Folding points of unimodal inverse limit spaces
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Bibliographic record
Abstract
Abstract Williams’ work from the 1960s and 1970s provides a thorough understanding of hyperbolic one-dimensional attractors through their representation as inverse limits. In fact, point in a uniformly hyperbolic attractor has a neighbourhood that is homeomorphic to a Cantor set of open arcs. In order to understand the topology of non-uniformly hyperbolic attractors better, we study the existence and prevalence of points with more complicated local structures in simple models of planar attractors, focusing on unimodal inverse limits setting. Such points whose neighbourhoods are not homeomorphic to the product of a Cantor set and an open arc are called folding points. We distinguish between various types of folding points and study how the dynamics of the underlying unimodal map affects their structures. Specifically, we characterise unimodal inverse limit spaces for which every folding point is an endpoint.
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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 | 0.001 |
| 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) | 0.001 | 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