{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZVD2PBBRBX3M4TT6TNKXBH2MGX","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":"bc56bb9a683975385c3c9b29d0a57f3b0ec3b6507df1b6d9d62a63bce490ad6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-05-26T01:33:58Z","title_canon_sha256":"29c29ecdb72c27490f246ce05fc2a68bdf09e2049535a6f8819279ccb0e91484"},"schema_version":"1.0","source":{"id":"1105.5186","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5186","created_at":"2026-05-18T03:37:20Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5186v1","created_at":"2026-05-18T03:37:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5186","created_at":"2026-05-18T03:37:20Z"},{"alias_kind":"pith_short_12","alias_value":"ZVD2PBBRBX3M","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZVD2PBBRBX3M4TT6","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZVD2PBBR","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:bf98f5a6240c6b66cc3f9395203361dccadfd4579a2a276c396bb5273c64038c","target":"graph","created_at":"2026-05-18T03:37:20Z","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"},"paper":{"abstract_excerpt":"In this paper, we state and prove precise theorems on the classification of the category of (braided) categorical groups and their (braided) monoidal functors, and some applications obtained from the basic studies on monoidal functors between categorical groups.","authors_text":"Nguyen Thu Thuy, Nguyen Tien Quang, Pham Thi Cuc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-05-26T01:33:58Z","title":"On monoidal functors between (braided) Gr-categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5186","kind":"arxiv","version":1},"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:e335319fdbdb6bb2dce38d912f999ca7164eeefa6acc0fb11f5d5468e2d4ff85","target":"record","created_at":"2026-05-18T03:37:20Z","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":"bc56bb9a683975385c3c9b29d0a57f3b0ec3b6507df1b6d9d62a63bce490ad6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-05-26T01:33:58Z","title_canon_sha256":"29c29ecdb72c27490f246ce05fc2a68bdf09e2049535a6f8819279ccb0e91484"},"schema_version":"1.0","source":{"id":"1105.5186","kind":"arxiv","version":1}},"canonical_sha256":"cd47a784310df6ce4e7e9b55709f4c35dd8a7c4d547ec0ea2878c02227c63d83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd47a784310df6ce4e7e9b55709f4c35dd8a7c4d547ec0ea2878c02227c63d83","first_computed_at":"2026-05-18T03:37:20.415437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:20.415437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N8B9h6J8E1LWtFHOR4dFO1iNOa3zLxXKdP9LMRlOgrgVNVASgRyzdp4ZaFUhPou3H2b6LdRXMXHLOuSmSgYrCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:20.415891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.5186","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e335319fdbdb6bb2dce38d912f999ca7164eeefa6acc0fb11f5d5468e2d4ff85","sha256:bf98f5a6240c6b66cc3f9395203361dccadfd4579a2a276c396bb5273c64038c"],"state_sha256":"6260e6bd5c94b53e66cf7cab21e640d188d56b9a4c094ef2f5a5e7d7bd185557"}