Bibliographic record
Abstract
Abstract We develop a general theory of 3-dimensional “orbifold completion”, to describe (generalised) orbifolds of topological quantum field theories as well as all their defects. Given a semistrict 3-category $$\mathcal {T}$$ T with adjoints for all 1- and 2-morphisms (more precisely, a Gray category with duals), we construct the 3-category $${\mathcal {T}}_{\text {orb}}$$ T orb as a Morita category of certain $$E_1$$ E 1 -algebras in $$\mathcal {T}$$ T which encode triangulation invariance. We prove that in $${\mathcal {T}}_{\text {orb}}$$ T orb again all 1- and 2-morphisms have adjoints, that it contains $$\mathcal {T}$$ T as a full subcategory, and we argue, but do not prove, that it satisfies a universal property which implies $${({\mathcal {T}}_{\text {orb}})}_{\text {orb}} \cong {\mathcal {T}}_{\text {orb}}$$ ( T orb ) orb ≅ T orb . This is a categorification of the work in Carquevill and Runkel (Quantum Topol 7(2):203–279, 2016). Orbifold completion by design allows us to lift the orbifold construction from closed TQFT to the much richer world of defect TQFTs. We illustrate this by constructing a universal 3-dimensional state sum model with all defects from first principles, and we explain how recent work on defects between Witt equivalent Reshetikhin–Turaev theories naturally appears as a special case of orbifold completion.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot 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.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".