{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IYFUXXKCYM5GUNFSWNQ7UWWPVQ","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":"21b9b449b94fb7b12a851c2429ff9b92ab3d72f630e10bfc4928d632ce34e6b0","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-11-08T14:57:18Z","title_canon_sha256":"8a2f5e31996b5dc8d5bf9b13851136e3c83e8d03bc780eea8c55939c0a6c4300"},"schema_version":"1.0","source":{"id":"1511.02491","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02491","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02491v3","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02491","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"pith_short_12","alias_value":"IYFUXXKCYM5G","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"IYFUXXKCYM5GUNFS","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"IYFUXXKC","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:040c8192b7881bb70a1e39f025973904cab19538521bd3fd5363ac48de631cde","target":"graph","created_at":"2026-05-18T01:09:55Z","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":"We survey the concept of multiplicativity from its initial appearance in the theory of Poisson-Lie groups to the far-reaching generalizations, for multivectors and differential forms in the geometry and the generalized geometry of Lie groupoids, as well as their infinitesimal counterparts in the theory of Lie algebroids.","authors_text":"Yvette Kosmann-Schwarzbach","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-11-08T14:57:18Z","title":"Multiplicativity, from Lie groups to generalized geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02491","kind":"arxiv","version":3},"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":"sha256:60c0c4c185dd9aab4f2cee4fb6a22a087c12e9e11b1c4b6fcd77e1a7d4ce031a","target":"record","created_at":"2026-05-18T01:09:55Z","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":"21b9b449b94fb7b12a851c2429ff9b92ab3d72f630e10bfc4928d632ce34e6b0","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-11-08T14:57:18Z","title_canon_sha256":"8a2f5e31996b5dc8d5bf9b13851136e3c83e8d03bc780eea8c55939c0a6c4300"},"schema_version":"1.0","source":{"id":"1511.02491","kind":"arxiv","version":3}},"canonical_sha256":"460b4bdd42c33a6a34b2b361fa5acfac1a597f37ed61eb63693eee481d0708ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"460b4bdd42c33a6a34b2b361fa5acfac1a597f37ed61eb63693eee481d0708ca","first_computed_at":"2026-05-18T01:09:55.133400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:55.133400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YB85NOOAyPUAvVPvPtBe7a84KHga6J58tC+G0v/1AnKv797/bu9JymRvpnV+e6QBqCCaiUegUtgk0lyr5gbzDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:55.133941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.02491","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60c0c4c185dd9aab4f2cee4fb6a22a087c12e9e11b1c4b6fcd77e1a7d4ce031a","sha256:040c8192b7881bb70a1e39f025973904cab19538521bd3fd5363ac48de631cde"],"state_sha256":"2989f5e3e1838db2581d9fa8e13394aa8ea6dc31efaad28e0a8c0beb4e28fdd8"}