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Record W4404357898 · doi:10.1017/fms.2024.102

The spin Brauer category

2024· article· en· W4404357898 on OpenAlexfundno aff
Peter J. McNamara, Alistair Savage

Bibliographic record

VenueForum of Mathematics Sigma · 2024
Typearticle
Languageen
FieldMathematics
TopicAlgebraic structures and combinatorial models
Canadian institutionsnot available
FundersAustralian Research CouncilNatural Sciences and Engineering Research Council of CanadaStanley Medical Research Institute
KeywordsMathematicsBrauer groupSpin (aerodynamics)Pure mathematicsPhysics

Abstract

fetched live from OpenAlex

Abstract We introduce a diagrammatic monoidal category, the spin Brauer category , that plays the same role for the spin and pin groups as the Brauer category does for the orthogonal groups. In particular, there is a full functor from the spin Brauer category to the category of finite-dimensional modules for the spin and pin groups. This functor becomes essentially surjective after passing to the Karoubi envelope, and its kernel is the tensor ideal of negligible morphisms. In this way, the spin Brauer category can be thought of as an interpolating category for the spin and pin groups. We also define an affine version of the spin Brauer category, which acts on categories of modules for the pin and spin groups via translation functors.

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 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)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation 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 score0.206
Threshold uncertainty score0.457

Codex and Gemma teacher scores by category

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

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 head0.023
GPT teacher head0.299
Teacher spread0.276 · 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 teacher head, 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

Citations1
Published2024
Admission routes1
Has abstractyes

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