Computing defects associated to bounded domain wall structures: the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Z</mml:mi> <mml:mo>/</mml:mo> <mml:mi>p</mml:mi> <mml:mi>Z</mml:mi> </mml:math> case
Bibliographic record
Abstract
Abstract We discuss domain walls and defects in topological phases occurring as the Drinfeld center of some fusion category. Domain walls between such phases correspond to bimodules between the fusion categories. Point defects correspond to functors between the bimodules. A domain wall structure consists of a planar graph with faces labeled by fusion categories. Edges are labeled by bimodules. When the vertices are labeled by point defects we get a compound defect. We present an algorithm, called the domain wall structure algorithm, for computing the compound defect. We apply this algorithm to show that the bimodule associator , related to the O 3 obstruction of Etingof et al (2010 Quantum Topol . 1 209), is trivial for all domain walls of Vec Z / p Z . In the language of this paper, the ground states of the Levin–Wen model are compound defects. We use this to define a generalization of the Levin–Wen model with domain walls and point defects. The domain wall structure algorithm can be used to compute the ground states of these generalized Levin–Wen type models.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".