{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:2EBDC2O7TAEI5ZPJLQDJUBDQ2U","short_pith_number":"pith:2EBDC2O7","schema_version":"1.0","canonical_sha256":"d1023169df98088ee5e95c069a0470d5130c355b2798db477f9afeee874695cc","source":{"kind":"arxiv","id":"1008.2505","version":1},"attestation_state":"computed","paper":{"title":"Introduction to co-split Lie algebras","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Limeng Xia, Naihong Hu","submitted_at":"2010-08-15T08:49:51Z","abstract_excerpt":"In this work, we introduce a new concept which is obtained by defining a new compatibility condition between Lie algebras and Lie coalgebras. With this terminology, we describe the interrelation between the Killing form and the adjoint representation in a new perspective."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1008.2505","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.QA","submitted_at":"2010-08-15T08:49:51Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"ff2547fb15668e00535315c81ac7921db77d7d3892f7d11fdb79c96f202af418","abstract_canon_sha256":"b27a9ecf7edd300090d4af6654277d1aab52c5f3e485eebaed414952d24b5318"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:38.403369Z","signature_b64":"Oom5S5dxfU3TP447Rg0+oIwaEY/ksv0S06eICfAwcF447l9hughebOcosnbf572ip/i0uFeWecXzeHkIwruoBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1023169df98088ee5e95c069a0470d5130c355b2798db477f9afeee874695cc","last_reissued_at":"2026-05-18T03:58:38.402921Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:38.402921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Introduction to co-split Lie algebras","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Limeng Xia, Naihong Hu","submitted_at":"2010-08-15T08:49:51Z","abstract_excerpt":"In this work, we introduce a new concept which is obtained by defining a new compatibility condition between Lie algebras and Lie coalgebras. With this terminology, we describe the interrelation between the Killing form and the adjoint representation in a new perspective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2505","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1008.2505","created_at":"2026-05-18T03:58:38.402981+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.2505v1","created_at":"2026-05-18T03:58:38.402981+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2505","created_at":"2026-05-18T03:58:38.402981+00:00"},{"alias_kind":"pith_short_12","alias_value":"2EBDC2O7TAEI","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"2EBDC2O7TAEI5ZPJ","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"2EBDC2O7","created_at":"2026-05-18T12:26:03.138858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2EBDC2O7TAEI5ZPJLQDJUBDQ2U","json":"https://pith.science/pith/2EBDC2O7TAEI5ZPJLQDJUBDQ2U.json","graph_json":"https://pith.science/api/pith-number/2EBDC2O7TAEI5ZPJLQDJUBDQ2U/graph.json","events_json":"https://pith.science/api/pith-number/2EBDC2O7TAEI5ZPJLQDJUBDQ2U/events.json","paper":"https://pith.science/paper/2EBDC2O7"},"agent_actions":{"view_html":"https://pith.science/pith/2EBDC2O7TAEI5ZPJLQDJUBDQ2U","download_json":"https://pith.science/pith/2EBDC2O7TAEI5ZPJLQDJUBDQ2U.json","view_paper":"https://pith.science/paper/2EBDC2O7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.2505&json=true","fetch_graph":"https://pith.science/api/pith-number/2EBDC2O7TAEI5ZPJLQDJUBDQ2U/graph.json","fetch_events":"https://pith.science/api/pith-number/2EBDC2O7TAEI5ZPJLQDJUBDQ2U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2EBDC2O7TAEI5ZPJLQDJUBDQ2U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2EBDC2O7TAEI5ZPJLQDJUBDQ2U/action/storage_attestation","attest_author":"https://pith.science/pith/2EBDC2O7TAEI5ZPJLQDJUBDQ2U/action/author_attestation","sign_citation":"https://pith.science/pith/2EBDC2O7TAEI5ZPJLQDJUBDQ2U/action/citation_signature","submit_replication":"https://pith.science/pith/2EBDC2O7TAEI5ZPJLQDJUBDQ2U/action/replication_record"}},"created_at":"2026-05-18T03:58:38.402981+00:00","updated_at":"2026-05-18T03:58:38.402981+00:00"}