Endperiodic maps, splitting sequences, and branched surfaces
Bibliographic record
Abstract
We strengthen the unpublished theorem of Gabai and Mosher that every depth one sutured manifold contains a very full dynamic branched surface by showing that the branched surface can be chosen to satisfy an additional property we call veering.To this end we prove that every endperiodic map admits a periodic splitting sequence of train tracks carrying its positive Handel-Miller lamination.This completes step one of Gabai and Mosher's unpublished two-step proof that every taut finite-depth foliation of a compact, oriented, atoroidal 3-manifold is almost transverse to a pseudo-Anosov flow.Further, a veering branched surface in a sutured manifold is a generalization of a veering triangulation, and we extend some of the theory of veering triangulations to this setting.In particular we show that the branched surfaces we construct are unique up to a natural equivalence relation, and give an algorithmic way to compute the foliation cones of Cantwell and Conlon.37E30, 57K32 1. Introduction 4532 2. Train tracks and laminations 4537 3. Endperiodic maps 4553 4. Periodic sequences of endperiodic train tracks 4562 5. Endperiodic maps and sutured manifolds 4572 6. Veering branched surfaces 4576 7. Veering branched surfaces for Handel-Miller laminations 4595 8. Foliation cones 4610 9. Uniqueness of veering branched surfaces which carry Handel-Miller laminations 4616 10.Examples
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".