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In particular, the conjecture that holomorphic permutation orbifolds are non-anomalous and therefore a stronger conjecture of M\\\"uger about braided crossed $S_n$-categories arising from permutation orbifolds of completely rational conformal nets are wrong. More general, we show that cyclic permutations of order $n$ are non-anomalous if and only if $3\\nmid n$ or $24"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1812.11910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-31T17:34:14Z","cross_cats_sorted":["math.MP","math.QA"],"title_canon_sha256":"8e7b3dbd15e256e1b6205106d68085b554ef7761484ae5ac91a64000510df49a","abstract_canon_sha256":"082d57de89a85b2e3f1d25b418cc585f62807eaf43e65a85bf3b92865314fda9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:10.792883Z","signature_b64":"gd5j/b1BCZgyITllYtGU8tsFlra9xCXzrWZjzRhV/bWQvS06XM5yVkBUjOKZnpvM0Xq6HS+NurlUz1uWYak7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13e28df3dcc1ed2ff373f7990ea1c5541301083951a984319ec78528409702fb","last_reissued_at":"2026-05-17T23:57:10.792539Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:10.792539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A remark about the anomalies of cyclic holomorphic permutation orbifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.QA"],"primary_cat":"math-ph","authors_text":"Marcel Bischoff","submitted_at":"2018-12-31T17:34:14Z","abstract_excerpt":"Using a result of Longo and Xu, we show that the anomaly arising from a cyclic permutation orbifold of order 3 of a holomorphic conformal net $\\mathcal A$ with central charge $c=8k$ depends on the \"gravitational anomaly\" $k\\pmod 3$. In particular, the conjecture that holomorphic permutation orbifolds are non-anomalous and therefore a stronger conjecture of M\\\"uger about braided crossed $S_n$-categories arising from permutation orbifolds of completely rational conformal nets are wrong. 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