{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LZOR5SWXXY5WPVQQFOGZPFV2WX","short_pith_number":"pith:LZOR5SWX","canonical_record":{"source":{"id":"1709.08582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-25T16:35:15Z","cross_cats_sorted":[],"title_canon_sha256":"37f9292ba4d6af39ca5de212598dad82af4354cde4a06f7bff69d53d45e4abb9","abstract_canon_sha256":"9ace1eadd716f797ee3b25c74fbf19c83783c7aa45bed6ab30a40e7009773dd7"},"schema_version":"1.0"},"canonical_sha256":"5e5d1ecad7be3b67d6102b8d9796bab5ff4b693c3ed4a87160e797d23fe7ec53","source":{"kind":"arxiv","id":"1709.08582","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08582","created_at":"2026-05-18T00:34:25Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08582v1","created_at":"2026-05-18T00:34:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08582","created_at":"2026-05-18T00:34:25Z"},{"alias_kind":"pith_short_12","alias_value":"LZOR5SWXXY5W","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LZOR5SWXXY5WPVQQ","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LZOR5SWX","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LZOR5SWXXY5WPVQQFOGZPFV2WX","target":"record","payload":{"canonical_record":{"source":{"id":"1709.08582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-25T16:35:15Z","cross_cats_sorted":[],"title_canon_sha256":"37f9292ba4d6af39ca5de212598dad82af4354cde4a06f7bff69d53d45e4abb9","abstract_canon_sha256":"9ace1eadd716f797ee3b25c74fbf19c83783c7aa45bed6ab30a40e7009773dd7"},"schema_version":"1.0"},"canonical_sha256":"5e5d1ecad7be3b67d6102b8d9796bab5ff4b693c3ed4a87160e797d23fe7ec53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:25.255432Z","signature_b64":"uxN97j6ChN4l7i8ufpXgw4RaCdR8D1Xsly57jRTL/6LNYp1MkDNlBIN3F9sWDD/1M1nsxHcYW/E8KNHPYxvNBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e5d1ecad7be3b67d6102b8d9796bab5ff4b693c3ed4a87160e797d23fe7ec53","last_reissued_at":"2026-05-18T00:34:25.254925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:25.254925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.08582","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":"2026-05-18T00:34:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d2EkXtjJQdgFDUrv3OsxLsUa0UZDFf9YCeYenxj9QiVRnAhcaF8MgJV93p9YJO2nrCtoO54ezWa7zDM9EYKeDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T13:11:35.364696Z"},"content_sha256":"fbd9cae3291edb22dced8deb18277df518af0cb3635f54b92f2a73f45d0cbe49","schema_version":"1.0","event_id":"sha256:fbd9cae3291edb22dced8deb18277df518af0cb3635f54b92f2a73f45d0cbe49"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LZOR5SWXXY5WPVQQFOGZPFV2WX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Second Cohomology Group of Elementary Quadratic Lie Superalgebras and Classifying a Subclass of 8-dimensional Solvable Quadratic Lie Superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Cao Tran Tu Hai, Duong Minh Thanh, Le Anh Vu","submitted_at":"2017-09-25T16:35:15Z","abstract_excerpt":"By definition, a quadratic Lie superalgebra is a Lie superalgebra endowed with a non-degenerate supersymmetric bilinear form which satisfies the even and invariant properties. In this paper we calculate all of the second cohomology group of elementary quadratic Lie superalgebras which have been classified in \\cite{DU14} by applying the super-Poisson bracket on the super exterior algebra. Besides, we give the classification of 8-dimensional solvable quadratic Lie superalgebras having 6-dimensional indecomposable even part. The method is based on the double extension and classification results o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08582","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":"2026-05-18T00:34:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iVHBGdCkF2ls2tNtcm+Ut+/HswLXqh4NKJ7LD0MSRguOlGmG9/4SRjp/28qPsSvauhaDS9QDQh7Cte1pHTHGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T13:11:35.365233Z"},"content_sha256":"91221ec6f4753e842ac44c086c5cfe24fc52ac3d120040641f43f410c9d4a852","schema_version":"1.0","event_id":"sha256:91221ec6f4753e842ac44c086c5cfe24fc52ac3d120040641f43f410c9d4a852"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LZOR5SWXXY5WPVQQFOGZPFV2WX/bundle.json","state_url":"https://pith.science/pith/LZOR5SWXXY5WPVQQFOGZPFV2WX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LZOR5SWXXY5WPVQQFOGZPFV2WX/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":"2026-06-11T13:11:35Z","links":{"resolver":"https://pith.science/pith/LZOR5SWXXY5WPVQQFOGZPFV2WX","bundle":"https://pith.science/pith/LZOR5SWXXY5WPVQQFOGZPFV2WX/bundle.json","state":"https://pith.science/pith/LZOR5SWXXY5WPVQQFOGZPFV2WX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LZOR5SWXXY5WPVQQFOGZPFV2WX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LZOR5SWXXY5WPVQQFOGZPFV2WX","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":"9ace1eadd716f797ee3b25c74fbf19c83783c7aa45bed6ab30a40e7009773dd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-25T16:35:15Z","title_canon_sha256":"37f9292ba4d6af39ca5de212598dad82af4354cde4a06f7bff69d53d45e4abb9"},"schema_version":"1.0","source":{"id":"1709.08582","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08582","created_at":"2026-05-18T00:34:25Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08582v1","created_at":"2026-05-18T00:34:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08582","created_at":"2026-05-18T00:34:25Z"},{"alias_kind":"pith_short_12","alias_value":"LZOR5SWXXY5W","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LZOR5SWXXY5WPVQQ","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LZOR5SWX","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:91221ec6f4753e842ac44c086c5cfe24fc52ac3d120040641f43f410c9d4a852","target":"graph","created_at":"2026-05-18T00:34:25Z","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":"By definition, a quadratic Lie superalgebra is a Lie superalgebra endowed with a non-degenerate supersymmetric bilinear form which satisfies the even and invariant properties. In this paper we calculate all of the second cohomology group of elementary quadratic Lie superalgebras which have been classified in \\cite{DU14} by applying the super-Poisson bracket on the super exterior algebra. Besides, we give the classification of 8-dimensional solvable quadratic Lie superalgebras having 6-dimensional indecomposable even part. The method is based on the double extension and classification results o","authors_text":"Cao Tran Tu Hai, Duong Minh Thanh, Le Anh Vu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-25T16:35:15Z","title":"The Second Cohomology Group of Elementary Quadratic Lie Superalgebras and Classifying a Subclass of 8-dimensional Solvable Quadratic Lie Superalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08582","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:fbd9cae3291edb22dced8deb18277df518af0cb3635f54b92f2a73f45d0cbe49","target":"record","created_at":"2026-05-18T00:34:25Z","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":"9ace1eadd716f797ee3b25c74fbf19c83783c7aa45bed6ab30a40e7009773dd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-25T16:35:15Z","title_canon_sha256":"37f9292ba4d6af39ca5de212598dad82af4354cde4a06f7bff69d53d45e4abb9"},"schema_version":"1.0","source":{"id":"1709.08582","kind":"arxiv","version":1}},"canonical_sha256":"5e5d1ecad7be3b67d6102b8d9796bab5ff4b693c3ed4a87160e797d23fe7ec53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e5d1ecad7be3b67d6102b8d9796bab5ff4b693c3ed4a87160e797d23fe7ec53","first_computed_at":"2026-05-18T00:34:25.254925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:25.254925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uxN97j6ChN4l7i8ufpXgw4RaCdR8D1Xsly57jRTL/6LNYp1MkDNlBIN3F9sWDD/1M1nsxHcYW/E8KNHPYxvNBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:25.255432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.08582","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbd9cae3291edb22dced8deb18277df518af0cb3635f54b92f2a73f45d0cbe49","sha256:91221ec6f4753e842ac44c086c5cfe24fc52ac3d120040641f43f410c9d4a852"],"state_sha256":"c8d7cb5bd96c4fe64ac4508f89e047a45565ed6aea36841b19e23b5abc238e1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"syPAKeI8DkAlfjV7nCYkVCO7tncmPuEgNjDDs488s+8y/oxPqgw2rKTPZA4v8ZPhM959oH5Xz0lE4p4Jus3uDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T13:11:35.367368Z","bundle_sha256":"e452b54283a82a249a2fb6ec5df3340470b71f78e934af9d837e8f05ed4ef4a7"}}