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Record W3009610408 · doi:10.1093/imrn/rnaa325

Solid Ergodicity and Orbit Equivalence Rigidity for Coinduced Actions

2020· preprint· en· W3009610408 on OpenAlexafffund
Daniel Drimbe

Bibliographic record

VenueInternational Mathematics Research Notices · 2020
Typepreprint
Languageen
FieldMathematics
TopicAdvanced Operator Algebra Research
Canadian institutionsUniversity of Regina
FundersPacific Institute for the Mathematical Sciences
KeywordsErgodic theorySigmaMathematicsErgodicityEquivalence relationEquivalence (formal languages)Pure mathematicsOrbit (dynamics)Countable setRigidity (electromagnetism)PhysicsQuantum mechanicsStatistics

Abstract

fetched live from OpenAlex

Abstract We prove that the solid ergodicity property is stable with respect to taking coinduction for a fairly large class of coinduced action. More precisely, assume that $\Sigma <\Gamma $ are countable groups such that $g\Sigma g^{-1}\cap \Sigma $ is finite for any $g\in \Gamma \setminus \Sigma $. Then any measure preserving action $\Sigma \curvearrowright X_0$ gives rise to a solidly ergodic equivalence relation if and only if the equivalence relation of the associated coinduced action $\Gamma \curvearrowright X$ is solidly ergodic. We also obtain orbit equivalence rigidity for such actions by showing that the orbit equivalence relation of a rigid or compact measure preserving action $\Sigma \curvearrowright X_0$ of a property (T) group is “remembered” by the orbit equivalence relation of $\Gamma \curvearrowright X$.

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)0.001
metaresearch head score (Gemma)0.002
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 score0.005
Threshold uncertainty score0.016

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0010.001
Science and technology studies0.0020.004
Scholarly communication0.0020.003
Open science0.0010.004
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0050.000

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 head0.591
GPT teacher head0.600
Teacher spread0.009 · 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".

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Citations1
Published2020
Admission routes2
Has abstractyes

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Same venueInternational Mathematics Research NoticesSame topicAdvanced Operator Algebra ResearchFrench-language works237,207