{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:P6IZLXXV43333KVLB2WA4PZQQR","short_pith_number":"pith:P6IZLXXV","canonical_record":{"source":{"id":"1704.06810","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2017-04-22T15:19:10Z","cross_cats_sorted":[],"title_canon_sha256":"0486ba259c5ccbcf59044c9100caf473c555999c379e6ecb8e3f27233bf6c3d9","abstract_canon_sha256":"ca88dcc548193d9e0c33e06d469b2b2086d3de2b68a409b328ef0df904fcc162"},"schema_version":"1.0"},"canonical_sha256":"7f9195def5e6f7bdaaab0eac0e3f308460455673eadb291607ec79c1433ef6d6","source":{"kind":"arxiv","id":"1704.06810","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06810","created_at":"2026-05-18T00:24:02Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06810v4","created_at":"2026-05-18T00:24:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06810","created_at":"2026-05-18T00:24:02Z"},{"alias_kind":"pith_short_12","alias_value":"P6IZLXXV4333","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P6IZLXXV43333KVL","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P6IZLXXV","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:P6IZLXXV43333KVLB2WA4PZQQR","target":"record","payload":{"canonical_record":{"source":{"id":"1704.06810","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2017-04-22T15:19:10Z","cross_cats_sorted":[],"title_canon_sha256":"0486ba259c5ccbcf59044c9100caf473c555999c379e6ecb8e3f27233bf6c3d9","abstract_canon_sha256":"ca88dcc548193d9e0c33e06d469b2b2086d3de2b68a409b328ef0df904fcc162"},"schema_version":"1.0"},"canonical_sha256":"7f9195def5e6f7bdaaab0eac0e3f308460455673eadb291607ec79c1433ef6d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:02.391573Z","signature_b64":"hqq84Hl34+T90tfa7/4laqGlG5H2z4gV1YVdyGJc+MdxyBQKk9k7/rZfiskm1Y8RMRDlySm6X6LHPtnVDfnZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f9195def5e6f7bdaaab0eac0e3f308460455673eadb291607ec79c1433ef6d6","last_reissued_at":"2026-05-18T00:24:02.391064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:02.391064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.06810","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O2dxIwh8l1ycbA4dH6Qf2yn45C0w8ekUrDl4RgVQR29tlyMQbtTjtlp+osKikz9yVzow65yIV4DKSp3LdIywBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:24:22.421856Z"},"content_sha256":"69eda8cb6480fa2bc7a657995ea65079c87a11c870c25aa7bb0968482ddd83c9","schema_version":"1.0","event_id":"sha256:69eda8cb6480fa2bc7a657995ea65079c87a11c870c25aa7bb0968482ddd83c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:P6IZLXXV43333KVLB2WA4PZQQR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structures of Nichols (braided) Lie algebras of diagonal type","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Jing Wang, Shouchuan Zhang, Weicai Wu, Yao-Zhong Zhang","submitted_at":"2017-04-22T15:19:10Z","abstract_excerpt":"Let $V$ be a braided vector space of diagonal type. Let $\\mathfrak B(V)$, $\\mathfrak L^-(V)$ and $\\mathfrak L(V)$ be the Nichols algebra, Nichols Lie algebra and Nichols braided Lie algebra over $V$, respectively. We show that a monomial belongs to $\\mathfrak L(V)$ if and only if that this monomial is connected. We obtain the basis for $\\mathfrak L(V)$ of arithmetic root systems and the dimension for $\\mathfrak L(V)$ of finite Cartan type. We give the sufficient and necessary conditions for $\\mathfrak B(V) = F\\oplus \\mathfrak L^-(V)$ and $\\mathfrak L^-(V)= \\mathfrak L(V)$. We obtain an explici"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06810","kind":"arxiv","version":4},"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":"2026-05-18T00:24:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C2cRcLNFQiztk+/9kGhcSTFgZRVZDYc+Iy3SxV6kUUvN8s4FYCoWLok7FCwEnvvVFeziJ/W0le7SQwPzT+yPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:24:22.422572Z"},"content_sha256":"f093a461a55cee28eefb8bcda72f7d4d3390fbb2fa43226cb853052169bc1770","schema_version":"1.0","event_id":"sha256:f093a461a55cee28eefb8bcda72f7d4d3390fbb2fa43226cb853052169bc1770"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P6IZLXXV43333KVLB2WA4PZQQR/bundle.json","state_url":"https://pith.science/pith/P6IZLXXV43333KVLB2WA4PZQQR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P6IZLXXV43333KVLB2WA4PZQQR/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":"2026-05-26T09:24:22Z","links":{"resolver":"https://pith.science/pith/P6IZLXXV43333KVLB2WA4PZQQR","bundle":"https://pith.science/pith/P6IZLXXV43333KVLB2WA4PZQQR/bundle.json","state":"https://pith.science/pith/P6IZLXXV43333KVLB2WA4PZQQR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P6IZLXXV43333KVLB2WA4PZQQR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:P6IZLXXV43333KVLB2WA4PZQQR","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":"ca88dcc548193d9e0c33e06d469b2b2086d3de2b68a409b328ef0df904fcc162","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2017-04-22T15:19:10Z","title_canon_sha256":"0486ba259c5ccbcf59044c9100caf473c555999c379e6ecb8e3f27233bf6c3d9"},"schema_version":"1.0","source":{"id":"1704.06810","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06810","created_at":"2026-05-18T00:24:02Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06810v4","created_at":"2026-05-18T00:24:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06810","created_at":"2026-05-18T00:24:02Z"},{"alias_kind":"pith_short_12","alias_value":"P6IZLXXV4333","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P6IZLXXV43333KVL","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P6IZLXXV","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:f093a461a55cee28eefb8bcda72f7d4d3390fbb2fa43226cb853052169bc1770","target":"graph","created_at":"2026-05-18T00:24:02Z","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 $V$ be a braided vector space of diagonal type. Let $\\mathfrak B(V)$, $\\mathfrak L^-(V)$ and $\\mathfrak L(V)$ be the Nichols algebra, Nichols Lie algebra and Nichols braided Lie algebra over $V$, respectively. We show that a monomial belongs to $\\mathfrak L(V)$ if and only if that this monomial is connected. We obtain the basis for $\\mathfrak L(V)$ of arithmetic root systems and the dimension for $\\mathfrak L(V)$ of finite Cartan type. We give the sufficient and necessary conditions for $\\mathfrak B(V) = F\\oplus \\mathfrak L^-(V)$ and $\\mathfrak L^-(V)= \\mathfrak L(V)$. We obtain an explici","authors_text":"Jing Wang, Shouchuan Zhang, Weicai Wu, Yao-Zhong Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2017-04-22T15:19:10Z","title":"Structures of Nichols (braided) Lie algebras of diagonal type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06810","kind":"arxiv","version":4},"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":"sha256:69eda8cb6480fa2bc7a657995ea65079c87a11c870c25aa7bb0968482ddd83c9","target":"record","created_at":"2026-05-18T00:24:02Z","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":"ca88dcc548193d9e0c33e06d469b2b2086d3de2b68a409b328ef0df904fcc162","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2017-04-22T15:19:10Z","title_canon_sha256":"0486ba259c5ccbcf59044c9100caf473c555999c379e6ecb8e3f27233bf6c3d9"},"schema_version":"1.0","source":{"id":"1704.06810","kind":"arxiv","version":4}},"canonical_sha256":"7f9195def5e6f7bdaaab0eac0e3f308460455673eadb291607ec79c1433ef6d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f9195def5e6f7bdaaab0eac0e3f308460455673eadb291607ec79c1433ef6d6","first_computed_at":"2026-05-18T00:24:02.391064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:02.391064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hqq84Hl34+T90tfa7/4laqGlG5H2z4gV1YVdyGJc+MdxyBQKk9k7/rZfiskm1Y8RMRDlySm6X6LHPtnVDfnZCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:02.391573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06810","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69eda8cb6480fa2bc7a657995ea65079c87a11c870c25aa7bb0968482ddd83c9","sha256:f093a461a55cee28eefb8bcda72f7d4d3390fbb2fa43226cb853052169bc1770"],"state_sha256":"5f079c93c9940be0e83f0a7514dc803317d1d7e12eff171a5e63063a75050329"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UmHv8Bv3C/gewCr3Rfqn09yL07ieeLruV0Cc1VWAGGc7qZMj/f5fjx7PAlbS5dacgFHPMRdiYkewx4UpoiM8AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T09:24:22.426224Z","bundle_sha256":"33c061d1ad3f610c088daa4eed5da85a07b57fd08f56a13e8e0d8348725f9338"}}