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Record W2987184215 · doi:10.70930/tac/9wif9i8c

A modular functor from state sums for finite tensor categories and their bimodules

2022· article· en· W2987184215 on OpenAlex
Jürgen Fuchs, Gregor Schaumann, Christoph Schweigert

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.

venuePublished in a venue whose home country is Canada.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueTheory and applications of categories · 2022
Typearticle
Languageen
FieldMathematics
TopicAlgebraic structures and combinatorial models
Canadian institutionsnot available
FundersDeutsche Forschungsgemeinschaft
KeywordsFunctorBimoduleMathematicsTensor (intrinsic definition)Pure mathematicsExact functorModular designState (computer science)Tensor productClass (philosophy)Algebra over a fieldComputer scienceArtificial intelligenceAlgorithm

Abstract

fetched live from OpenAlex

We construct a modular functor which takes its values in the monoidal bicategory of finite categories, left exact functors and natural transformations.The modular functor is defined on bordisms that are 2-framed.Accordingly we do not need to require that the finite categories appearing in our construction are semisimple, nor that the finite tensor categories that are assigned to two-dimensional strata are endowed with a pivotal structure.Our prescription can be understood as a state-sum construction.The state-sum variables are assigned to one-dimensional strata and take values in bimodule categories over finite tensor categories, whereby we also account for the presence of boundaries and defects.Our construction allows us to explicitly compute functors associated to surfaces and representations of mapping class groups acting on them. Contents1 Introduction 437 2 Framed defect manifolds 442 3 Assigning categories to defect one-manifolds 456 4 Assigning functors to defect surfaces 473 5 The modular functor 505 A Framing shifts 556 B Categorical constructions 558 C Construction of a parallelization 568

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)0.000
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 score0.101
Threshold uncertainty score0.564

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 head0.016
GPT teacher head0.246
Teacher spread0.231 · 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