{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HFJDKRB7UDR33FD4Q5BCXPIAL4","short_pith_number":"pith:HFJDKRB7","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"},"canonical_sha256":"395235443fa0e3bd947c87422bbd005f2c1fd8f798e04419410b6f1c429c86fa","source":{"kind":"arxiv","id":"1307.2540","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HFJDKRB7UDR33FD4Q5BCXPIAL4","target":"record","payload":{"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"},"canonical_sha256":"395235443fa0e3bd947c87422bbd005f2c1fd8f798e04419410b6f1c429c86fa","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"},"source_kind":"arxiv","source_id":"1307.2540","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AUX4KMtqnAvRIOAAOfuVVn+78fE52Pl3KkrPBs2EW8d+kSSWKZZpHsFn3skNr1nDEsBqWH9i2O37d4KxrHDXBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:51:44.740270Z"},"content_sha256":"733e141d526b41a7b7880770b995252253689bedcf622c60834cb6397d6f71e4","schema_version":"1.0","event_id":"sha256:733e141d526b41a7b7880770b995252253689bedcf622c60834cb6397d6f71e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HFJDKRB7UDR33FD4Q5BCXPIAL4","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RfjF+sLs2q2aPqD0xxGfn/3xMRhIO3egMa9RXoZDNBiTVQTPomD1APw+36YbKAbJWlMv3X6LriQM0vo3c2fkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:51:44.740631Z"},"content_sha256":"38e2bc8847ed30652462a073470d28fa4d7658b3f4ead2de4e3ea7f066ed624d","schema_version":"1.0","event_id":"sha256:38e2bc8847ed30652462a073470d28fa4d7658b3f4ead2de4e3ea7f066ed624d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4/bundle.json","state_url":"https://pith.science/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4/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":"2026-06-24T02:51:44Z","links":{"resolver":"https://pith.science/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4","bundle":"https://pith.science/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4/bundle.json","state":"https://pith.science/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HFJDKRB7UDR33FD4Q5BCXPIAL4/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Js94w5TujTPnHTuQeepn0f3sAyw7Xgllw338q+McpwLVPsoikW4vu5TSvjvyMZUbwjCwa6KkBu1N95oLwHHKBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T02:51:44.743478Z","bundle_sha256":"30c3547df06521791a91bfc6521a6900314ae6da7706d0e8d972eb6c6f7ae3c0"}}