{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QVTOD7TBIHJRHY4GZA7TBTGZB6","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":"ced20f81e81487527dd17c584b7fd99e01f30deab9ff6ed8c45d4e3f535174ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-17T12:48:30Z","title_canon_sha256":"e414af54041d1c49a967f597a3b050d213a82625581641580e1214e5762fe74e"},"schema_version":"1.0","source":{"id":"1904.08237","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.08237","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"arxiv_version","alias_value":"1904.08237v1","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.08237","created_at":"2026-05-17T23:48:18Z"},{"alias_kind":"pith_short_12","alias_value":"QVTOD7TBIHJR","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QVTOD7TBIHJRHY4G","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QVTOD7TB","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:dc247ac70d39af5673ba12e546f866e04b89c927f02e8a9018866d4b0f33521b","target":"graph","created_at":"2026-05-17T23:48:18Z","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 show that the central representation is nontrivial for all one-dimensional central extensions of nilpotent Lie algebras possessing a codimension one abelian ideal.","authors_text":"Barry Jessup, Grant Cairns, Yuri Nikolayevsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-17T12:48:30Z","title":"A class of nilpotent Lie algebras whose center acts nontrivially in cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08237","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":"sha256:1289db004c8289864511ec1a17a0f12a73ff294399f8ed561c2e693816520763","target":"record","created_at":"2026-05-17T23:48:18Z","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":"ced20f81e81487527dd17c584b7fd99e01f30deab9ff6ed8c45d4e3f535174ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-17T12:48:30Z","title_canon_sha256":"e414af54041d1c49a967f597a3b050d213a82625581641580e1214e5762fe74e"},"schema_version":"1.0","source":{"id":"1904.08237","kind":"arxiv","version":1}},"canonical_sha256":"8566e1fe6141d313e386c83f30ccd90f9f803fc7b8e853d59455f08008e39b8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8566e1fe6141d313e386c83f30ccd90f9f803fc7b8e853d59455f08008e39b8c","first_computed_at":"2026-05-17T23:48:18.292986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:18.292986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u/u1NsONtD6pxfQTQJ0MPzhqQjUtdJpUG3TteQaUqnkpEXrhs/nbUh2vWxYmDlGyU+ET2mp7lxSUsqG/uq0RBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:18.293443Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.08237","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1289db004c8289864511ec1a17a0f12a73ff294399f8ed561c2e693816520763","sha256:dc247ac70d39af5673ba12e546f866e04b89c927f02e8a9018866d4b0f33521b"],"state_sha256":"8acba65fd00e9f21f72e11c4e254ddd57c28d0a180ea4080622dd131e89876e2"}