Pith Number

pith:YIAKQJGD

pith:2026:YIAKQJGDBVGAF5VRZBPHFJTR4V

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Examples of Invertible Gauging via Orbifold Data, Zesting, and Equivariantisation

Benjamin Haake

Zested orbifold data for symmetries related by zesting are Morita-equivalent and share the same surface defect.

arxiv:2605.16942 v1 · 2026-05-16 · hep-th · math-ph · math.MP · math.QA

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\pithnumber{YIAKQJGDBVGAF5VRZBPHFJTR4V}

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Claims

C1strongest claim

We introduce zested orbifold data for symmetries related by zesting and show that the two associated orbifold data are Morita-equivalent, i.e. they have the same underlying surface defect.

C2weakest assumption

The assumption that the generalised orbifold construction, equivariantisation, and G-crossed braided zesting can be applied consistently to the listed symmetries (Z2 in D(Z2), Tambara-Yamagami categories, and central symmetry in SU(2)_k Chern-Simons) without hidden obstructions beyond those already discussed.

C3one line summary

Illustrates relations among gauging methods for invertible symmetries in 3D TQFTs and proves Morita equivalence of zested orbifold data for related symmetries.

References

96 extracted · 96 resolved · 19 Pith anchors

[1] Turaev, Vladimir , doi =

[2] On braided fusion categories I · arXiv:0906.0620

[3] Module categories over the Drinfeld double of a finite group 2003 · doi:10.1155/s1073792803205079

[4] Tensor categories , url =

[5] The pivotal cover and Frobenius-Schur indicators 2015 · doi:10.1016/j.jalgebra.2015.01.014

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:32.063592Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c200a824c30d4c02f6b1c85e72a671e56ea60869e3ebecc86651a81e406fb9cd

Aliases

arxiv: 2605.16942 · arxiv_version: 2605.16942v1 · doi: 10.48550/arxiv.2605.16942 · pith_short_12: YIAKQJGDBVGA · pith_short_16: YIAKQJGDBVGAF5VR · pith_short_8: YIAKQJGD

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YIAKQJGDBVGAF5VRZBPHFJTR4V \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c200a824c30d4c02f6b1c85e72a671e56ea60869e3ebecc86651a81e406fb9cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c42e0d76200b94fb5de526ccea2d36edc1df43b9f9811c9c436d5c03e6c5961e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.QA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2026-05-16T11:27:49Z",
    "title_canon_sha256": "4dc0a23b9d5956b0193bb1672940ab8169ebc8c9b81dd0ba34da31cfe30b90df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16942",
    "kind": "arxiv",
    "version": 1
  }
}