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Record W4404961356 · doi:10.1007/s00208-024-03048-8

Graph manifolds that admit arbitrarily many Anosov flows

2024· article· en· W4404961356 on OpenAlexafffund
Adam Clay, Tali Pinsky

Bibliographic record

VenueMathematische Annalen · 2024
Typearticle
Languageen
FieldMathematics
TopicMathematical Dynamics and Fractals
Canadian institutionsUniversity of Manitoba
FundersNatural Sciences and Engineering Research Council of CanadaTechnion-Israel Institute of TechnologyIsrael Science Foundation
KeywordsMathematicsGraphPure mathematicsCombinatorics

Abstract

fetched live from OpenAlex

Abstract For each natural number n, we construct an example of a graph manifold supporting at least n different Anosov flows that are not orbit equivalent. Our construction is reminiscent of the Thurston-Handel construction [11]: we cut a geodesic flow on a surface of constant negative curvature into two pieces, modify the flow in each piece by pulling back to finite covers, and glue together compatible pairs of pullback flows along their boundary tori to get many distinct flows on the resulting graph manifold.

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 imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.001
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.002
Threshold uncertainty score0.005

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0000.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0010.000
Science and technology studies0.0010.002
Scholarly communication0.0010.001
Open science0.0000.002
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0020.000

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.

Opus teacher head0.065
GPT teacher head0.317
Teacher spread0.252 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations2
Published2024
Admission routes2
Has abstractyes

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