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Record W1668462598 · doi:10.2140/pjm.2016.281.365

Good traces for not necessarily simple dimension groups

2016· article· en· W1668462598 on OpenAlexaff
David Handelman

Bibliographic record

VenuePacific Journal of Mathematics · 2016
Typearticle
Languageen
FieldMathematics
TopicAdvanced Operator Algebra Research
Canadian institutionsUniversity of Ottawa
Fundersnot available
KeywordsMathematicsSimple (philosophy)Dimension (graph theory)ConjecturePure mathematicsAlgebraic numberEffective dimensionMeasure (data warehouse)Complex dimensionGroup (periodic table)Algebra over a fieldHausdorff dimensionMathematical analysisComputer science

Abstract

fetched live from OpenAlex

Akin's notion of good measure, introduced to classify measures on Cantor sets, has been translated to dimension groups and traces by Bezuglyi and the author, but emphasizing the simple (minimal dynamical system) case.Here we permit nonsimplicity.Goodness of tensor products of large classes of non-good traces (measures) is established.We also determine the pure faithful good traces on the dimension groups associated to xerox-type actions on AF C*-algebras; the criteria turn out to involve algebraic geometry and number theory.We also deal with a coproduct of dimension groups, wherein, despite expectations, goodness of direct sums is nontrivial.In addition, we verify a conjecture of Bezuglyi and Handelman (2014) concerning good subsets of Choquet simplices, in the finite-dimensional case.Introduction and definitions 365 1. Characterization of goodness 368 2. Tensor products 373 3. Examples from xerox actions of tori on UHF algebras 379 4. Direct sums and goodness 389 5. Good sets of traces 398 Appendix A. Connections with zero-dimensional topological dynamics 408 Appendix B. Order unit good traces on ‫ޚ‬ k 412 Appendix C. Good simplices

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)0.003
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 score0.004
Threshold uncertainty score0.011

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.003
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0030.001
Science and technology studies0.0020.006
Scholarly communication0.0040.006
Open science0.0010.003
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0030.000

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 head0.062
GPT teacher head0.352
Teacher spread0.289 · 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

Citations3
Published2016
Admission routes1
Has abstractyes

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Same venuePacific Journal of MathematicsSame topicAdvanced Operator Algebra ResearchFrench-language works237,207