{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:D6LWOCZOHTJYYY632BSAKM7XO7","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":"938930f3392953955a40fe89c19293d4454d19d1173474c6354a6ddbe75b42b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-10-10T13:37:05Z","title_canon_sha256":"a86d75d2ae9babbf154fbbd6124983e879eb9ba2085fb28108f618990916ace2"},"schema_version":"1.0","source":{"id":"1410.2778","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2778","created_at":"2026-05-18T02:40:37Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2778v1","created_at":"2026-05-18T02:40:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2778","created_at":"2026-05-18T02:40:37Z"},{"alias_kind":"pith_short_12","alias_value":"D6LWOCZOHTJY","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D6LWOCZOHTJYYY63","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D6LWOCZO","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:d32f0c340c4fccfc9b5a412361564412b26b08f02ad5d45d780e14c6218dccfe","target":"graph","created_at":"2026-05-18T02:40:37Z","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":"A Lie algebra $L$ is said to be of breadth $k$ if the maximal dimension of the images of left multiplication by elements of the algebra is $k$. In this paper we give characterization of finite dimensional nilpotent Lie algebras of breadth less than or equal to two. Furthermore, using these characterizations we determined the isomorphism classes of these algebras.","authors_text":"Borworn Khuhirun, Ernie Stitzinger, Kailash C. Misra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-10-10T13:37:05Z","title":"On nilpotent Lie algebras of small breadth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2778","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":"sha256:08144d7991c53800db485e4d7c00dae0a59fc67664ff89ca58c84259c5ed9aae","target":"record","created_at":"2026-05-18T02:40:37Z","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":"938930f3392953955a40fe89c19293d4454d19d1173474c6354a6ddbe75b42b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-10-10T13:37:05Z","title_canon_sha256":"a86d75d2ae9babbf154fbbd6124983e879eb9ba2085fb28108f618990916ace2"},"schema_version":"1.0","source":{"id":"1410.2778","kind":"arxiv","version":1}},"canonical_sha256":"1f97670b2e3cd38c63dbd0640533f777fb2786bf0a29746b6ab5d4f1383e9e63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f97670b2e3cd38c63dbd0640533f777fb2786bf0a29746b6ab5d4f1383e9e63","first_computed_at":"2026-05-18T02:40:37.209834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:37.209834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"idhnqAE2oxpFkdqYpO/rgx3rOMvYaAiK1QigyHBg4GlC0rpKCtQcVRbkEqTgHKOJwcC2/ExL0WYF0X1N6KHkBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:37.210562Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2778","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08144d7991c53800db485e4d7c00dae0a59fc67664ff89ca58c84259c5ed9aae","sha256:d32f0c340c4fccfc9b5a412361564412b26b08f02ad5d45d780e14c6218dccfe"],"state_sha256":"1277a945c08bd74333da3b03d042a8d2f7870b1ead485d4240106dc4896d17ca"}