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For the fusion category $\\mathcal{C} $ which is the even part of the self-dual $3^{\\mathbb{Z}/2\\mathbb{Z} \\times \\mathbb{Z}/2\\mathbb{Z} } $ subfactor, we show that there are $30$ simple module categories over $ \\mathcal{C}$; there are no other fusion categories in the Morita equivalence class; and the order of the Brauer-Picard group is $360$. The proof proceeds indirectly by first describing the Brauer-Picard groupoid of a $ \\mathb"},"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":"1612.07185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-12-21T15:29:08Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"c1f66a0086c2ff91742f9b9aa58c91b8728f38ffacff4315b6b377b9208535cc","abstract_canon_sha256":"5b5ffed590ed94d331a2a6c5100c1c3127de79a92380922327349e033684d188"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:14.488196Z","signature_b64":"7SN2ZS/l9HojKPhauPMt+oVJvHd2snJUZQ3EzFHqK0tS3eRqTIRsPEFA3hWUjBXvhbom8gnlyxbM6JUcXkDoCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9102fe7739f22d8ee3d5da9eb5d1b7de3d49d39e7af06a9aec69fbcdaf194715","last_reissued_at":"2026-05-18T00:54:14.487621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:14.487621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fusion Categories Associated to Subfactors with Index $3+\\sqrt{5}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"Pinhas Grossman","submitted_at":"2016-12-21T15:29:08Z","abstract_excerpt":"We classify fusion categories which are Morita equivalent to even parts of subfactors with index $3+\\sqrt{5} $, and module categories over these fusion categories. 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