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Record W3130614675 · doi:10.1093/imrn/rnaa282

Uniform Property Γ

2020· article· en· W3130614675 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueInternational Mathematics Research Notices · 2020
Typearticle
Languageen
FieldMathematics
TopicAdvanced Operator Algebra Research
Canadian institutionsWilfrid Laurier UniversityUniversity of Ottawa
FundersEngineering and Physical Sciences Research CouncilVlaamse regeringNarodowe Centrum NaukiAlexander von Humboldt-Stiftung
KeywordsMathematicsConjectureProperty (philosophy)Separable spacePure mathematicsEquivalence (formal languages)Space (punctuation)Mathematical analysis

Abstract

fetched live from OpenAlex

Abstract We further examine the concept of uniform property $\Gamma $ for $C^*$-algebras introduced in our joint work with Winter. In addition to obtaining characterisations in the spirit of Dixmier’s work on central sequences in II$_1$ factors, we establish the equivalence of uniform property $\Gamma $, a suitable uniform version of McDuff’s property for $C^*$-algebras, and the existence of complemented partitions of unity for separable nuclear $C^*$-algebras with no finite dimensional representations and a compact (non-empty) tracial state space. As a consequence, for $C^*$-algebras as in the Toms–Winter conjecture, the combination of strict comparison and uniform property $\Gamma $ is equivalent to Jiang–Su stability. We also show how these ideas can be combined with those of Matui–Sato to streamline Winter’s classification by embeddings technique.

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.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.010
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMetaresearch, Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.495
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.010
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.001
Open science0.0020.001
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0020.001

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 head0.371
GPT teacher head0.493
Teacher spread0.121 · 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