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Record W1659214574 · doi:10.1139/p02-020

The RacahWigner category

2002· article· en· W1659214574 on OpenAlexvenueno aff
William P. Joyce, Philip H. Butler, H J Ross

Bibliographic record

VenueCanadian Journal of Physics · 2002
Typearticle
Languageen
FieldComputer Science
TopicLogic, programming, and type systems
Canadian institutionsnot available
FundersMarsden Fund
KeywordsDiagrammatic reasoningCategory theoryPure mathematicsLemma (botany)DiagramFactorizationPhysicsDecompositionAlgebra over a fieldCalculus (dental)MathematicsLinguistics

Abstract

fetched live from OpenAlex

The Racah–Wigner calculus is formulated using category theory. The notion of recoupling requires a consistent choice of isomorphisms corresponding to regrouping of irreducible representations. This is the essential content of a ring category. Hence the Racah–Wigner calculus is inherently a ring category. Category theory places the emphasis on maps between representations. The diagrammatic approach of category theory lays bare underlying relationships in the Racah–Wigner calculus. Direct sum decomposition, coupling coefficients, recoupling coefficients, and group chain decomposition are simplified and clarified when represented by diagrams. The diagram techniques of category theory are unlike diagram techniques used for group calculations. The Biedenharn–Elliott sum rule, Racah backcoupling, Racah factorisation lemma, and the Wigner–Eckart theorem are derived from properties of this category. PACS Nos.: 02.10Ws, 02.20Qs, 02.20Fh, 02.20Df, 03.65Fd, 31.15Hz

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: Methods · Consensus signal: none
Teacher disagreement score0.009
Threshold uncertainty score0.031

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0030.002
Science and technology studies0.0020.004
Scholarly communication0.0030.006
Open science0.0010.003
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0090.002

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 head0.027
GPT teacher head0.209
Teacher spread0.182 · 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
GenreMethods

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

Citations6
Published2002
Admission routes1
Has abstractyes

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