{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:WH5B63TJ7QVKW2O2JAFWYBZ4HQ","short_pith_number":"pith:WH5B63TJ","schema_version":"1.0","canonical_sha256":"b1fa1f6e69fc2aab69da480b6c073c3c2c310fcfcb241f7d8ed65d4d6e339a36","source":{"kind":"arxiv","id":"1910.03178","version":2},"attestation_state":"computed","paper":{"title":"Extension theory for braided-enriched fusion categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Corey Jones, David Penneys, Julia Plavnik, Scott Morrison","submitted_at":"2019-10-08T02:37:00Z","abstract_excerpt":"For a braided fusion category $\\mathcal{V}$, a $\\mathcal{V}$-fusion category is a fusion category $\\mathcal{C}$ equipped with a braided monoidal functor $\\mathcal{F}:\\mathcal{V} \\to Z(\\mathcal{C})$. Given a fixed $\\mathcal{V}$-fusion category $(\\mathcal{C}, \\mathcal{F})$ and a fixed $G$-graded extension $\\mathcal{C}\\subseteq \\mathcal{D}$ as an ordinary fusion category, we characterize the enrichments $\\widetilde{\\mathcal{F}}:\\mathcal{V} \\to Z(\\mathcal{D})$ of $\\mathcal{D}$ which are compatible with the enrichment of $\\mathcal{C}$. We show that G-crossed extensions of a braided fusion category "},"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":"1910.03178","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-10-08T02:37:00Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"276aba5bd9d4f4cdfdc38370a7da04a6cbc7bfa4637c77ce9d1b495f3008f9e6","abstract_canon_sha256":"0ad0e227dec6274305e7456e0cd9a88ddb8a41feb9d52941da9bde121401c292"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:35:00.049104Z","signature_b64":"5Y5IS4BrSyzeOG6ULOm6xkxTDnNcVVaVVOaobaZK7IIeA0jOWEpNvlPaOHWnrXluNJzVM5aL/AIaXBVFkt85DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1fa1f6e69fc2aab69da480b6c073c3c2c310fcfcb241f7d8ed65d4d6e339a36","last_reissued_at":"2026-07-05T02:35:00.048747Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:35:00.048747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extension theory for braided-enriched fusion categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Corey Jones, David Penneys, Julia Plavnik, Scott Morrison","submitted_at":"2019-10-08T02:37:00Z","abstract_excerpt":"For a braided fusion category $\\mathcal{V}$, a $\\mathcal{V}$-fusion category is a fusion category $\\mathcal{C}$ equipped with a braided monoidal functor $\\mathcal{F}:\\mathcal{V} \\to Z(\\mathcal{C})$. Given a fixed $\\mathcal{V}$-fusion category $(\\mathcal{C}, \\mathcal{F})$ and a fixed $G$-graded extension $\\mathcal{C}\\subseteq \\mathcal{D}$ as an ordinary fusion category, we characterize the enrichments $\\widetilde{\\mathcal{F}}:\\mathcal{V} \\to Z(\\mathcal{D})$ of $\\mathcal{D}$ which are compatible with the enrichment of $\\mathcal{C}$. We show that G-crossed extensions of a braided fusion category "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.03178","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.03178/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1910.03178","created_at":"2026-07-05T02:35:00.048801+00:00"},{"alias_kind":"arxiv_version","alias_value":"1910.03178v2","created_at":"2026-07-05T02:35:00.048801+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.03178","created_at":"2026-07-05T02:35:00.048801+00:00"},{"alias_kind":"pith_short_12","alias_value":"WH5B63TJ7QVK","created_at":"2026-07-05T02:35:00.048801+00:00"},{"alias_kind":"pith_short_16","alias_value":"WH5B63TJ7QVKW2O2","created_at":"2026-07-05T02:35:00.048801+00:00"},{"alias_kind":"pith_short_8","alias_value":"WH5B63TJ","created_at":"2026-07-05T02:35:00.048801+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.10603","citing_title":"The Classification of 3+1d Symmetry Enriched Topological Order","ref_index":63,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WH5B63TJ7QVKW2O2JAFWYBZ4HQ","json":"https://pith.science/pith/WH5B63TJ7QVKW2O2JAFWYBZ4HQ.json","graph_json":"https://pith.science/api/pith-number/WH5B63TJ7QVKW2O2JAFWYBZ4HQ/graph.json","events_json":"https://pith.science/api/pith-number/WH5B63TJ7QVKW2O2JAFWYBZ4HQ/events.json","paper":"https://pith.science/paper/WH5B63TJ"},"agent_actions":{"view_html":"https://pith.science/pith/WH5B63TJ7QVKW2O2JAFWYBZ4HQ","download_json":"https://pith.science/pith/WH5B63TJ7QVKW2O2JAFWYBZ4HQ.json","view_paper":"https://pith.science/paper/WH5B63TJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1910.03178&json=true","fetch_graph":"https://pith.science/api/pith-number/WH5B63TJ7QVKW2O2JAFWYBZ4HQ/graph.json","fetch_events":"https://pith.science/api/pith-number/WH5B63TJ7QVKW2O2JAFWYBZ4HQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WH5B63TJ7QVKW2O2JAFWYBZ4HQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WH5B63TJ7QVKW2O2JAFWYBZ4HQ/action/storage_attestation","attest_author":"https://pith.science/pith/WH5B63TJ7QVKW2O2JAFWYBZ4HQ/action/author_attestation","sign_citation":"https://pith.science/pith/WH5B63TJ7QVKW2O2JAFWYBZ4HQ/action/citation_signature","submit_replication":"https://pith.science/pith/WH5B63TJ7QVKW2O2JAFWYBZ4HQ/action/replication_record"}},"created_at":"2026-07-05T02:35:00.048801+00:00","updated_at":"2026-07-05T02:35:00.048801+00:00"}