{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HFJDKRB7UDR33FD4Q5BCXPIAL4","short_pith_number":"pith:HFJDKRB7","schema_version":"1.0","canonical_sha256":"395235443fa0e3bd947c87422bbd005f2c1fd8f798e04419410b6f1c429c86fa","source":{"kind":"arxiv","id":"1307.2540","version":3},"attestation_state":"computed","paper":{"title":"Unified products for Leibniz algebras. Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.RA","authors_text":"A.L. Agore, G. Militaru","submitted_at":"2013-07-09T18:46:47Z","abstract_excerpt":"Let $\\mathfrak{g}$ be a Leibniz algebra and $E$ a vector space containing $\\mathfrak{g}$ as a subspace. All Leibniz algebra structures on $E$ containing $\\mathfrak{g}$ as a subalgebra are explicitly described and classified by two non-abelian cohomological type objects: ${\\mathcal H}{\\mathcal L}^{2}_{\\mathfrak{g}} \\, (V, \\, \\mathfrak{g})$ provides the classification up to an isomorphism that stabilizes $\\mathfrak{g}$ and ${\\mathcal H}{\\mathcal L}^{2} \\, (V, \\, \\mathfrak{g})$ will classify all such structures from the view point of the extension problem - here $V$ is a complement of $\\mathfrak{"},"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":"1307.2540","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-09T18:46:47Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"c642d2ba85563ef85ca2ab558a58d7dc0a9b79a333beb728879e59c322190a64","abstract_canon_sha256":"dbb60ef53b5b3d582b3e29b38a5fd3d357e2dae1e431e3dae1619c29d28d1d96"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:23.500954Z","signature_b64":"z3TzLY/lLJ6vpF+0Mnua4URK+SuiJv7oKLqOojofiiBmmOGtEdvO9dZ3F5yHN9k5YYiAEcUNU/jsxLufMD58Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"395235443fa0e3bd947c87422bbd005f2c1fd8f798e04419410b6f1c429c86fa","last_reissued_at":"2026-05-18T02:58:23.500395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:23.500395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unified products for Leibniz algebras. Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.RA","authors_text":"A.L. Agore, G. Militaru","submitted_at":"2013-07-09T18:46:47Z","abstract_excerpt":"Let $\\mathfrak{g}$ be a Leibniz algebra and $E$ a vector space containing $\\mathfrak{g}$ as a subspace. All Leibniz algebra structures on $E$ containing $\\mathfrak{g}$ as a subalgebra are explicitly described and classified by two non-abelian cohomological type objects: ${\\mathcal H}{\\mathcal L}^{2}_{\\mathfrak{g}} \\, (V, \\, \\mathfrak{g})$ provides the classification up to an isomorphism that stabilizes $\\mathfrak{g}$ and ${\\mathcal H}{\\mathcal L}^{2} \\, (V, \\, \\mathfrak{g})$ will classify all such structures from the view point of the extension problem - here $V$ is a complement of $\\mathfrak{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2540","kind":"arxiv","version":3},"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":"1307.2540","created_at":"2026-05-18T02:58:23.500474+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.2540v3","created_at":"2026-05-18T02:58:23.500474+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2540","created_at":"2026-05-18T02:58:23.500474+00:00"},{"alias_kind":"pith_short_12","alias_value":"HFJDKRB7UDR3","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HFJDKRB7UDR33FD4","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HFJDKRB7","created_at":"2026-05-18T12:27:46.883200+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/HFJDKRB7UDR33FD4Q5BCXPIAL4","json":"https://pith.science/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4.json","graph_json":"https://pith.science/api/pith-number/HFJDKRB7UDR33FD4Q5BCXPIAL4/graph.json","events_json":"https://pith.science/api/pith-number/HFJDKRB7UDR33FD4Q5BCXPIAL4/events.json","paper":"https://pith.science/paper/HFJDKRB7"},"agent_actions":{"view_html":"https://pith.science/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4","download_json":"https://pith.science/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4.json","view_paper":"https://pith.science/paper/HFJDKRB7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.2540&json=true","fetch_graph":"https://pith.science/api/pith-number/HFJDKRB7UDR33FD4Q5BCXPIAL4/graph.json","fetch_events":"https://pith.science/api/pith-number/HFJDKRB7UDR33FD4Q5BCXPIAL4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4/action/storage_attestation","attest_author":"https://pith.science/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4/action/author_attestation","sign_citation":"https://pith.science/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4/action/citation_signature","submit_replication":"https://pith.science/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4/action/replication_record"}},"created_at":"2026-05-18T02:58:23.500474+00:00","updated_at":"2026-05-18T02:58:23.500474+00:00"}