{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:K65THHMPOMXC3L67J2YL6HSSUY","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":"570dd0672f12ce52bbcec93bcb377708d33fc425077c98f3460d561790eda766","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2005-05-31T16:28:49Z","title_canon_sha256":"f9e8e0c51b58b534a66667995bda28cbc8a329ef09d866d123cd2ccecd242f5c"},"schema_version":"1.0","source":{"id":"math/0505688","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0505688","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/0505688v2","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0505688","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"pith_short_12","alias_value":"K65THHMPOMXC","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"K65THHMPOMXC3L67","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"K65THHMP","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:ec98a345090bee7c67b83e77e8776c924759d27f7398d213b7f56792b607b9d9","target":"graph","created_at":"2026-05-18T02:57:36Z","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 math.DG/0312243 we developed a general classification scheme for metric Lie algebras, i.e. for finite-dimensional Lie algebras equipped with a non-degenerate invariant inner product. Here we determine all nilpotent Lie algebras l with dim l'=2 which are used in this scheme. Furthermore, we classify all nilpotent metric Lie algebras of dimension at most 10.","authors_text":"Ines Kath","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2005-05-31T16:28:49Z","title":"Nilpotent metric Lie algebras of small dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505688","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":"sha256:079ed50af00a40869c232d2b23b6ff6c2c9dcf818206e9eb84b7d4ed9a930d21","target":"record","created_at":"2026-05-18T02:57:36Z","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":"570dd0672f12ce52bbcec93bcb377708d33fc425077c98f3460d561790eda766","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2005-05-31T16:28:49Z","title_canon_sha256":"f9e8e0c51b58b534a66667995bda28cbc8a329ef09d866d123cd2ccecd242f5c"},"schema_version":"1.0","source":{"id":"math/0505688","kind":"arxiv","version":2}},"canonical_sha256":"57bb339d8f732e2dafdf4eb0bf1e52a62a9dc08435a0a9b8bd0af6c0c89d3ff2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57bb339d8f732e2dafdf4eb0bf1e52a62a9dc08435a0a9b8bd0af6c0c89d3ff2","first_computed_at":"2026-05-18T02:57:36.323889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:36.323889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H4w/w+opQ6Bci973XfyoAPylwrNzs86IxDnZ5UW2wZp9HSj7k2Y7niE3t1cHhPpxvpgr9sBC7q3Pi8ll+b+fCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:36.324449Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0505688","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:079ed50af00a40869c232d2b23b6ff6c2c9dcf818206e9eb84b7d4ed9a930d21","sha256:ec98a345090bee7c67b83e77e8776c924759d27f7398d213b7f56792b607b9d9"],"state_sha256":"22167fe9be66489a969cf390c0d52a3a231bd78161ec9a0652bb4ec83e6068a0"}