{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:M772RCVYTOFYJWM3MFQTFS7QOC","short_pith_number":"pith:M772RCVY","schema_version":"1.0","canonical_sha256":"67ffa88ab89b8b84d99b616132cbf070bcb5b541e3d59c4967dff0c69dad8dc2","source":{"kind":"arxiv","id":"2103.15150","version":2},"attestation_state":"computed","paper":{"title":"Weak Fusion 2-Categories","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Thibault D. D\\'ecoppet","submitted_at":"2021-03-28T15:16:17Z","abstract_excerpt":"We introduce a weakening of the notion of fusion 2-category given in arXiv:1812.11933. Then, we establish a number of properties of (multi)fusion 2-categories. Finally, we describe the fusion rule of the fusion 2-categories associated to certain pointed braided fusion categories."},"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":"2103.15150","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2021-03-28T15:16:17Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"636be46a2125dc9197061f2d1e16aae2be4f9d04a159d23005e7c0c5846cb4c7","abstract_canon_sha256":"a163e9460e27a81db27e1897e9252b647007a3de85a3a8a8c35c86897fe2f61c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:14:08.335587Z","signature_b64":"La9UEiFmBj1M6eRla0bO1coO3Lbs4+I/uV+fGZkC0/Ewd3l+Gy/nzVEdLHu1Ww2DaEwU/ewy0HNvDhTYKgS0DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67ffa88ab89b8b84d99b616132cbf070bcb5b541e3d59c4967dff0c69dad8dc2","last_reissued_at":"2026-07-05T05:14:08.335119Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:14:08.335119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak Fusion 2-Categories","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Thibault D. D\\'ecoppet","submitted_at":"2021-03-28T15:16:17Z","abstract_excerpt":"We introduce a weakening of the notion of fusion 2-category given in arXiv:1812.11933. Then, we establish a number of properties of (multi)fusion 2-categories. Finally, we describe the fusion rule of the fusion 2-categories associated to certain pointed braided fusion categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.15150","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/2103.15150/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":"2103.15150","created_at":"2026-07-05T05:14:08.335170+00:00"},{"alias_kind":"arxiv_version","alias_value":"2103.15150v2","created_at":"2026-07-05T05:14:08.335170+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.15150","created_at":"2026-07-05T05:14:08.335170+00:00"},{"alias_kind":"pith_short_12","alias_value":"M772RCVYTOFY","created_at":"2026-07-05T05:14:08.335170+00:00"},{"alias_kind":"pith_short_16","alias_value":"M772RCVYTOFYJWM3","created_at":"2026-07-05T05:14:08.335170+00:00"},{"alias_kind":"pith_short_8","alias_value":"M772RCVY","created_at":"2026-07-05T05:14:08.335170+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2204.02407","citing_title":"Higher Gauging and Non-invertible Condensation Defects","ref_index":61,"is_internal_anchor":false},{"citing_arxiv_id":"2308.00747","citing_title":"What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries","ref_index":242,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M772RCVYTOFYJWM3MFQTFS7QOC","json":"https://pith.science/pith/M772RCVYTOFYJWM3MFQTFS7QOC.json","graph_json":"https://pith.science/api/pith-number/M772RCVYTOFYJWM3MFQTFS7QOC/graph.json","events_json":"https://pith.science/api/pith-number/M772RCVYTOFYJWM3MFQTFS7QOC/events.json","paper":"https://pith.science/paper/M772RCVY"},"agent_actions":{"view_html":"https://pith.science/pith/M772RCVYTOFYJWM3MFQTFS7QOC","download_json":"https://pith.science/pith/M772RCVYTOFYJWM3MFQTFS7QOC.json","view_paper":"https://pith.science/paper/M772RCVY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2103.15150&json=true","fetch_graph":"https://pith.science/api/pith-number/M772RCVYTOFYJWM3MFQTFS7QOC/graph.json","fetch_events":"https://pith.science/api/pith-number/M772RCVYTOFYJWM3MFQTFS7QOC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M772RCVYTOFYJWM3MFQTFS7QOC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M772RCVYTOFYJWM3MFQTFS7QOC/action/storage_attestation","attest_author":"https://pith.science/pith/M772RCVYTOFYJWM3MFQTFS7QOC/action/author_attestation","sign_citation":"https://pith.science/pith/M772RCVYTOFYJWM3MFQTFS7QOC/action/citation_signature","submit_replication":"https://pith.science/pith/M772RCVYTOFYJWM3MFQTFS7QOC/action/replication_record"}},"created_at":"2026-07-05T05:14:08.335170+00:00","updated_at":"2026-07-05T05:14:08.335170+00:00"}