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Record W3040402236 · doi:10.4171/jca/55

Group partition categories

2021· preprint· en· W3040402236 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

VenueJournal of Combinatorial Algebra · 2021
Typepreprint
Languageen
FieldMathematics
TopicAlgebraic structures and combinatorial models
Canadian institutionsUniversity of Ottawa
Fundersnot available
KeywordsWreath productMathematicsMorphismPartition (number theory)EmbeddingEnriched categoryCombinatoricsGroup (periodic table)Symmetric groupSymmetric monoidal categoryCategory of groupsClosed monoidal categoryPure mathematicsDiscrete mathematicsProduct (mathematics)Computer scienceAbelian groupPhysicsGeometry

Abstract

fetched live from OpenAlex

To every group G we associate a linear monoidal category \mathcal{P}\textit{ar}(G) that we call a group partition category . We give explicit bases for the morphism spaces and also an efficient presentation of the category in terms of generators and relations. We then define an embedding of \mathcal{P}\textit{ar}(G) into the group Heisenberg category associated to G . This embedding intertwines the natural actions of both categories on modules for wreath products of G . Finally, we prove that the additive Karoubi envelope of \mathcal{P}\textit{ar}(G) is equivalent to a wreath product interpolating category introduced by Knop, thereby giving a simple concrete description of that category.

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)0.001
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
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 score0.061
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0020.001
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.001
Research integrity0.0010.002
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 head0.031
GPT teacher head0.290
Teacher spread0.259 · 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