{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:A3VDB5SCTASD6KTNTIMRAKXNMG","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":"2ca327a522d5ed50357c171bd7378ae15911ba2a2b40b7fade1bd5058ecbfd57","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-03-27T16:41:39Z","title_canon_sha256":"b8ac51e6971b43912090612bfd5eae841f19b7903129ffa1839a377d96c6b76c"},"schema_version":"1.0","source":{"id":"1203.6018","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6018","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6018v1","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6018","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"pith_short_12","alias_value":"A3VDB5SCTASD","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"A3VDB5SCTASD6KTN","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"A3VDB5SC","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:99369d00283a11a73355de828ac9e06dda07cad52ec3f3bab0fd26d63bb43218","target":"graph","created_at":"2026-05-18T03:59:12Z","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 give a criterion for the Kostant-Kirillov form on an adjoint orbit in a real semisimple Lie group to be exact. We explicitly compute the second cohomology of all the nilpotent adjoint orbits in every complex simple Lie algebras.","authors_text":"Indranil Biswas, Pralay Chatterjee","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-03-27T16:41:39Z","title":"On the exactness of Kostant-Kirillov form and the second cohomology of nilpotent orbits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6018","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":"sha256:4b58eae7e9c7423e3a7f39369a6b16b87bcbfc889ad322fdcf7a101d6421d04b","target":"record","created_at":"2026-05-18T03:59:12Z","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":"2ca327a522d5ed50357c171bd7378ae15911ba2a2b40b7fade1bd5058ecbfd57","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-03-27T16:41:39Z","title_canon_sha256":"b8ac51e6971b43912090612bfd5eae841f19b7903129ffa1839a377d96c6b76c"},"schema_version":"1.0","source":{"id":"1203.6018","kind":"arxiv","version":1}},"canonical_sha256":"06ea30f64298243f2a6d9a19102aed61822921ef82713ebb17627ff043c5f665","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06ea30f64298243f2a6d9a19102aed61822921ef82713ebb17627ff043c5f665","first_computed_at":"2026-05-18T03:59:12.719700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:12.719700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v3brLj2imw3ffh/NUfVKnASbdY0VUj4JCzFGScCi6NClYu9V4g+auPx4qNB9yRVCAMfT6wxC3oscwggASF98BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:12.720171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6018","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b58eae7e9c7423e3a7f39369a6b16b87bcbfc889ad322fdcf7a101d6421d04b","sha256:99369d00283a11a73355de828ac9e06dda07cad52ec3f3bab0fd26d63bb43218"],"state_sha256":"727229460c4498db0c76379fee41106a2faf158b360bcfb4828a91e91595fcb2"}