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Record W4402684764 · doi:10.1142/s0218216524500366

Equivalence of field theories: Crane–Yetter and the shadow

2024· article· en· W4402684764 on OpenAlexaff
Jin-Cheng Guu

Bibliographic record

VenueJournal of Knot Theory and Its Ramifications · 2024
Typearticle
Languageen
FieldMathematics
TopicHistory and Theory of Mathematics
Canadian institutionsUniversity of Alberta
Fundersnot available
KeywordsMathematicsEquivalence (formal languages)Shadow (psychology)Field (mathematics)Pure mathematicsAlgebra over a fieldCalculus (dental)OrthodonticsPsychology

Abstract

fetched live from OpenAlex

This work solves a 28-year conjecture by showing that two major invariants of smooth 4-manifolds, the shadow model (motivated by statistical mechanics [V. G. Turaev, Topology of shadows (1991)]) and the simplicial Crane–Yetter model (motivated by topological quantum field theory [L. Crane and D. Yetter, A categorical construction of 4D topological quantum field theories, in Quantum Topology (World Scientific, 1993), pp. 120–130, https://doi.org/10.1142/9789812796387_0005 ]), are in fact equal. These invariants, both of which degenerate to the 3D Witten–Reshetikhin–Turaev model in a special case, had been open for years to clarify their relationship. Despite the seeming difference in their origins and formal constructions, we prove their equivalence. Along the way, we sketch a dictionary between the two models, provide a brief survey of the shadow construction à la Turaev, and suggest once again that the semisimple models have reached their limits.

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)0.004
metaresearch head score (Gemma)0.002
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 score0.242
Threshold uncertainty score0.259

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0040.002
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 head0.029
GPT teacher head0.311
Teacher spread0.282 · 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

Citations0
Published2024
Admission routes1
Has abstractyes

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