{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:D6LWOCZOHTJYYY632BSAKM7XO7","short_pith_number":"pith:D6LWOCZO","canonical_record":{"source":{"id":"1410.2778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-10-10T13:37:05Z","cross_cats_sorted":[],"title_canon_sha256":"a86d75d2ae9babbf154fbbd6124983e879eb9ba2085fb28108f618990916ace2","abstract_canon_sha256":"938930f3392953955a40fe89c19293d4454d19d1173474c6354a6ddbe75b42b1"},"schema_version":"1.0"},"canonical_sha256":"1f97670b2e3cd38c63dbd0640533f777fb2786bf0a29746b6ab5d4f1383e9e63","source":{"kind":"arxiv","id":"1410.2778","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:D6LWOCZOHTJYYY632BSAKM7XO7","target":"record","payload":{"canonical_record":{"source":{"id":"1410.2778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-10-10T13:37:05Z","cross_cats_sorted":[],"title_canon_sha256":"a86d75d2ae9babbf154fbbd6124983e879eb9ba2085fb28108f618990916ace2","abstract_canon_sha256":"938930f3392953955a40fe89c19293d4454d19d1173474c6354a6ddbe75b42b1"},"schema_version":"1.0"},"canonical_sha256":"1f97670b2e3cd38c63dbd0640533f777fb2786bf0a29746b6ab5d4f1383e9e63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:37.210562Z","signature_b64":"idhnqAE2oxpFkdqYpO/rgx3rOMvYaAiK1QigyHBg4GlC0rpKCtQcVRbkEqTgHKOJwcC2/ExL0WYF0X1N6KHkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f97670b2e3cd38c63dbd0640533f777fb2786bf0a29746b6ab5d4f1383e9e63","last_reissued_at":"2026-05-18T02:40:37.209834Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:37.209834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.2778","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EizIUtWuQQyd7GNitb5Ch81thNp5QVc+Rq8NO7lxk3paJLZznKc1JYSmBUjo8hmzSuHuvchquMPGpnocVoYiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T13:20:13.808774Z"},"content_sha256":"08144d7991c53800db485e4d7c00dae0a59fc67664ff89ca58c84259c5ed9aae","schema_version":"1.0","event_id":"sha256:08144d7991c53800db485e4d7c00dae0a59fc67664ff89ca58c84259c5ed9aae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:D6LWOCZOHTJYYY632BSAKM7XO7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On nilpotent Lie algebras of small breadth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Borworn Khuhirun, Ernie Stitzinger, Kailash C. Misra","submitted_at":"2014-10-10T13:37:05Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2778","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jswav/YR3ae9g6piTfKJ72Rwp54cJm3Y4BviEMZIemmGH+GbN1VJMnhEtkWdm7J1BhPQQtyAkY1LweFQScibBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T13:20:13.809119Z"},"content_sha256":"d32f0c340c4fccfc9b5a412361564412b26b08f02ad5d45d780e14c6218dccfe","schema_version":"1.0","event_id":"sha256:d32f0c340c4fccfc9b5a412361564412b26b08f02ad5d45d780e14c6218dccfe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D6LWOCZOHTJYYY632BSAKM7XO7/bundle.json","state_url":"https://pith.science/pith/D6LWOCZOHTJYYY632BSAKM7XO7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D6LWOCZOHTJYYY632BSAKM7XO7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T13:20:13Z","links":{"resolver":"https://pith.science/pith/D6LWOCZOHTJYYY632BSAKM7XO7","bundle":"https://pith.science/pith/D6LWOCZOHTJYYY632BSAKM7XO7/bundle.json","state":"https://pith.science/pith/D6LWOCZOHTJYYY632BSAKM7XO7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D6LWOCZOHTJYYY632BSAKM7XO7/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vH9YBYPGMZ05Q1re5SlO5pbt8+TuuEoC0uYKIIXaGXCHw3ek7eUZ8i3sKzkPnofBTlkJUjFaXp3CGWx9tK7qDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T13:20:13.811082Z","bundle_sha256":"94616a5887947187d4fbe1f44a8ea31e291c28ce0769e49ab6c672eddc27c7bf"}}