{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:M772RCVYTOFYJWM3MFQTFS7QOC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a163e9460e27a81db27e1897e9252b647007a3de85a3a8a8c35c86897fe2f61c","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2021-03-28T15:16:17Z","title_canon_sha256":"636be46a2125dc9197061f2d1e16aae2be4f9d04a159d23005e7c0c5846cb4c7"},"schema_version":"1.0","source":{"id":"2103.15150","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.15150","created_at":"2026-07-05T05:14:08Z"},{"alias_kind":"arxiv_version","alias_value":"2103.15150v2","created_at":"2026-07-05T05:14:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.15150","created_at":"2026-07-05T05:14:08Z"},{"alias_kind":"pith_short_12","alias_value":"M772RCVYTOFY","created_at":"2026-07-05T05:14:08Z"},{"alias_kind":"pith_short_16","alias_value":"M772RCVYTOFYJWM3","created_at":"2026-07-05T05:14:08Z"},{"alias_kind":"pith_short_8","alias_value":"M772RCVY","created_at":"2026-07-05T05:14:08Z"}],"graph_snapshots":[{"event_id":"sha256:9c585f56d25a7ce77f83df88e55d08e9acda10af4f7c6575f547d4b2addf71dd","target":"graph","created_at":"2026-07-05T05:14:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2103.15150/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Thibault D. D\\'ecoppet","cross_cats":["math.CT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2021-03-28T15:16:17Z","title":"Weak Fusion 2-Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.15150","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8c60f2828ac168180f4148d2b81b9c03eadd7091e257134b6fc8dfb9591942b2","target":"record","created_at":"2026-07-05T05:14:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a163e9460e27a81db27e1897e9252b647007a3de85a3a8a8c35c86897fe2f61c","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.QA","submitted_at":"2021-03-28T15:16:17Z","title_canon_sha256":"636be46a2125dc9197061f2d1e16aae2be4f9d04a159d23005e7c0c5846cb4c7"},"schema_version":"1.0","source":{"id":"2103.15150","kind":"arxiv","version":2}},"canonical_sha256":"67ffa88ab89b8b84d99b616132cbf070bcb5b541e3d59c4967dff0c69dad8dc2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67ffa88ab89b8b84d99b616132cbf070bcb5b541e3d59c4967dff0c69dad8dc2","first_computed_at":"2026-07-05T05:14:08.335119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:14:08.335119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"La9UEiFmBj1M6eRla0bO1coO3Lbs4+I/uV+fGZkC0/Ewd3l+Gy/nzVEdLHu1Ww2DaEwU/ewy0HNvDhTYKgS0DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:14:08.335587Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.15150","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c60f2828ac168180f4148d2b81b9c03eadd7091e257134b6fc8dfb9591942b2","sha256:9c585f56d25a7ce77f83df88e55d08e9acda10af4f7c6575f547d4b2addf71dd"],"state_sha256":"084cae9e89b9946b8ffe2a9c775985711db6b18aa823d614c147f609bcd8d0d8"}