{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HFJDKRB7UDR33FD4Q5BCXPIAL4","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":"dbb60ef53b5b3d582b3e29b38a5fd3d357e2dae1e431e3dae1619c29d28d1d96","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-09T18:46:47Z","title_canon_sha256":"c642d2ba85563ef85ca2ab558a58d7dc0a9b79a333beb728879e59c322190a64"},"schema_version":"1.0","source":{"id":"1307.2540","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2540","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2540v3","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2540","created_at":"2026-05-18T02:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"HFJDKRB7UDR3","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HFJDKRB7UDR33FD4","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HFJDKRB7","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:38e2bc8847ed30652462a073470d28fa4d7658b3f4ead2de4e3ea7f066ed624d","target":"graph","created_at":"2026-05-18T02:58:23Z","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":"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{","authors_text":"A.L. Agore, G. Militaru","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-09T18:46:47Z","title":"Unified products for Leibniz algebras. Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2540","kind":"arxiv","version":3},"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":"sha256:733e141d526b41a7b7880770b995252253689bedcf622c60834cb6397d6f71e4","target":"record","created_at":"2026-05-18T02:58:23Z","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":"dbb60ef53b5b3d582b3e29b38a5fd3d357e2dae1e431e3dae1619c29d28d1d96","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-09T18:46:47Z","title_canon_sha256":"c642d2ba85563ef85ca2ab558a58d7dc0a9b79a333beb728879e59c322190a64"},"schema_version":"1.0","source":{"id":"1307.2540","kind":"arxiv","version":3}},"canonical_sha256":"395235443fa0e3bd947c87422bbd005f2c1fd8f798e04419410b6f1c429c86fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"395235443fa0e3bd947c87422bbd005f2c1fd8f798e04419410b6f1c429c86fa","first_computed_at":"2026-05-18T02:58:23.500395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:23.500395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z3TzLY/lLJ6vpF+0Mnua4URK+SuiJv7oKLqOojofiiBmmOGtEdvO9dZ3F5yHN9k5YYiAEcUNU/jsxLufMD58Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:23.500954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2540","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:733e141d526b41a7b7880770b995252253689bedcf622c60834cb6397d6f71e4","sha256:38e2bc8847ed30652462a073470d28fa4d7658b3f4ead2de4e3ea7f066ed624d"],"state_sha256":"99fc1d0afd36c53e833d44cf863c425c34303577ebdc80d90e761384b171bf6a"}