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In particular, when $\\mathcal C$ is a root whose rank is the smallest in the family, $K$ becomes"},"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":"1908.02599","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-08-07T12:46:31Z","cross_cats_sorted":["math.CT","quant-ph"],"title_canon_sha256":"04fc84623ac3bea375c442eb63b57c20dc112f1745aa3c99ea09ab95c65afdf2","abstract_canon_sha256":"1de99563fd0478a13eef52edf13dad5efc91d157acd0f538f94e8a3b5faf6f6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:25:13.382219Z","signature_b64":"LAN9JAlkeVt+KSwUUNh6SfI3zJ+jP1fh88/GNgClDkpWMcS6Elu+NfqtWvW+Xscp72mY5zGoqA/QnSgL2JolAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b467b255e459291878affd939845a8d340031740adb440b17f9d9396f1be4de5","last_reissued_at":"2026-07-05T00:25:13.381789Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:25:13.381789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrix formulation for non-Abelian families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Tian Lan","submitted_at":"2019-08-07T12:46:31Z","abstract_excerpt":"We generalize the $K$ matrix formulation to non-trivial non-Abelian families of 2+1D topological orders. Given a topological order $\\mathcal C$, any topological order in the same non-Abelian family as $\\mathcal C$ can be efficiently described by $\\boldsymbol{a}=(a_I)$ where $a_I$ are Abelian anyons in $\\mathcal C$, together with a symmetric invertible matrix $K$, $K_{IJ}=k_{IJ}-t_{a_I,a_J}$ where $k_{IJ}$ are integers, $k_{II}$ are even and $t_{a_I,a_J}$ are the mutual statistics between $a_I,a_J$. 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