{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:O62WFLRIFAEAUZRVWWZ7OKPG47","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":"d9df9349676a6d07162ee0a3e4ba094a12212c999fcd86f759058b16688bd648","cross_cats_sorted":["math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-08T17:52:04Z","title_canon_sha256":"878024b22c1da0c6d81d82404caf1b3015f9d7098bb03b823487cca3cd48ee9b"},"schema_version":"1.0","source":{"id":"1212.1820","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1820","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1820v1","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1820","created_at":"2026-05-18T03:38:55Z"},{"alias_kind":"pith_short_12","alias_value":"O62WFLRIFAEA","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"O62WFLRIFAEAUZRV","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"O62WFLRI","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:1c76389c22708b95d9656fb8d1443aa19e78f3d0d345c4e7b0c14b22f5d1c230","target":"graph","created_at":"2026-05-18T03:38:55Z","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":"S-expansions of three-dimensional real Lie algebras are considered. It is shown that the expansion operation allows one to obtain a non-unimodular Lie algebra from a unimodular one. Nevertheless S-expansions define no ordering on the variety of Lie algebras of a fixed dimension.","authors_text":"Maryna Nesterenko","cross_cats":["math.MP","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-08T17:52:04Z","title":"S-expansions of three-dimensional Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1820","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:e1e50d88702935dbbcb27910741640d0918e690ec5527d2037f20d06f5bc244f","target":"record","created_at":"2026-05-18T03:38:55Z","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":"d9df9349676a6d07162ee0a3e4ba094a12212c999fcd86f759058b16688bd648","cross_cats_sorted":["math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-08T17:52:04Z","title_canon_sha256":"878024b22c1da0c6d81d82404caf1b3015f9d7098bb03b823487cca3cd48ee9b"},"schema_version":"1.0","source":{"id":"1212.1820","kind":"arxiv","version":1}},"canonical_sha256":"77b562ae2828080a6635b5b3f729e6e7d9a7d4b6502faaf31394f5a2659551d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77b562ae2828080a6635b5b3f729e6e7d9a7d4b6502faaf31394f5a2659551d5","first_computed_at":"2026-05-18T03:38:55.032644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:55.032644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Lf3TiiPMxY1XIOV3988yMJ0fo68caJEuURzIks+OHI3jFVf1mIh4ACuUZO/5DP45CM1zpknVryOmHxDw8/WDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:55.033212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1820","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1e50d88702935dbbcb27910741640d0918e690ec5527d2037f20d06f5bc244f","sha256:1c76389c22708b95d9656fb8d1443aa19e78f3d0d345c4e7b0c14b22f5d1c230"],"state_sha256":"03552fc64bcc2b652ebbbb4b18bbc952095e600a95de8045cd9777d0489a0d71"}