{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:T3ZJB7XMDR3SNXVLNPQJ7HOQUJ","short_pith_number":"pith:T3ZJB7XM","canonical_record":{"source":{"id":"1409.3769","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-09-12T15:25:52Z","cross_cats_sorted":[],"title_canon_sha256":"f69178ff5d9376bf1934f0cb6654d5f161c83c9474d5f86ea7021855fe0b2e16","abstract_canon_sha256":"1a0bfced03af7d26f57f3f53bfc9f1cdb4a54a5a8cf760b11629815cdd18c111"},"schema_version":"1.0"},"canonical_sha256":"9ef290feec1c7726deab6be09f9dd0a253bbbfa16a8e85b3cdb720cf245f9977","source":{"kind":"arxiv","id":"1409.3769","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3769","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3769v3","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3769","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"T3ZJB7XMDR3S","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T3ZJB7XMDR3SNXVL","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T3ZJB7XM","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:T3ZJB7XMDR3SNXVLNPQJ7HOQUJ","target":"record","payload":{"canonical_record":{"source":{"id":"1409.3769","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-09-12T15:25:52Z","cross_cats_sorted":[],"title_canon_sha256":"f69178ff5d9376bf1934f0cb6654d5f161c83c9474d5f86ea7021855fe0b2e16","abstract_canon_sha256":"1a0bfced03af7d26f57f3f53bfc9f1cdb4a54a5a8cf760b11629815cdd18c111"},"schema_version":"1.0"},"canonical_sha256":"9ef290feec1c7726deab6be09f9dd0a253bbbfa16a8e85b3cdb720cf245f9977","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:15.488271Z","signature_b64":"hRHH2sYfxRv8fFsXKbDTKQzCJ5w/+9NMyzCO/yOe4Nwek2DKhb8poTvr8rCzFP/5WyxIpyN59FcHXLbVMJddAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ef290feec1c7726deab6be09f9dd0a253bbbfa16a8e85b3cdb720cf245f9977","last_reissued_at":"2026-05-18T01:30:15.487493Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:15.487493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.3769","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":"2026-05-18T01:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qt7RsfSZpgsnS1/ZoELbVJYcY7MQ35WbYQaYDRnth1Z9sB/OZINITtSVR1BZ3dgkI1AEqVLIkyrNjL1a3jdIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:16:23.200059Z"},"content_sha256":"a0c551a6df5a62cf0d4b79446be6fbe2e4d2bd1bed71db2afe1ec7ee1ef5b0d7","schema_version":"1.0","event_id":"sha256:a0c551a6df5a62cf0d4b79446be6fbe2e4d2bd1bed71db2afe1ec7ee1ef5b0d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:T3ZJB7XMDR3SNXVLNPQJ7HOQUJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Nichols (braided) Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Shouchuan Zhang, Weicai Wu, Yao-Zhong Zhang","submitted_at":"2014-09-12T15:25:52Z","abstract_excerpt":"We prove {\\rm (i)} Nichols algebra $\\mathfrak B(V)$ of vector space $V$ is finite-dimensional if and only if Nichols braided Lie algebra $\\mathfrak L(V)$ is finite-dimensional; {\\rm (ii)} If the rank of connected $V$ is $2$ and $\\mathfrak B(V)$ is an arithmetic root system, then $\\mathfrak B(V) = F \\oplus \\mathfrak L(V);$ and {\\rm (iii)} if $\\Delta (\\mathfrak B(V))$ is an arithmetic root system and there does not exist any $m$-infinity element with $p_{uu} \\not= 1$ for any $u \\in D(V)$, then $\\dim (\\mathfrak B(V) ) = \\infty$ if and only if there exists $V'$, which is twisting equivalent to $V$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3769","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":"2026-05-18T01:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gF+EidB/qvnD7ZB7p+lB5B1m8a1SGcNS+grjN4KS1HuX3fKuxEc8HKiFszZq1GLjYaKp9ClTgUYcQ4Lm/NEwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:16:23.200700Z"},"content_sha256":"bce8d76276f854178a271df4bced4d6efa81ea12c0def1350470802d28d19936","schema_version":"1.0","event_id":"sha256:bce8d76276f854178a271df4bced4d6efa81ea12c0def1350470802d28d19936"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T3ZJB7XMDR3SNXVLNPQJ7HOQUJ/bundle.json","state_url":"https://pith.science/pith/T3ZJB7XMDR3SNXVLNPQJ7HOQUJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T3ZJB7XMDR3SNXVLNPQJ7HOQUJ/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":"2026-05-25T21:16:23Z","links":{"resolver":"https://pith.science/pith/T3ZJB7XMDR3SNXVLNPQJ7HOQUJ","bundle":"https://pith.science/pith/T3ZJB7XMDR3SNXVLNPQJ7HOQUJ/bundle.json","state":"https://pith.science/pith/T3ZJB7XMDR3SNXVLNPQJ7HOQUJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T3ZJB7XMDR3SNXVLNPQJ7HOQUJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:T3ZJB7XMDR3SNXVLNPQJ7HOQUJ","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":"1a0bfced03af7d26f57f3f53bfc9f1cdb4a54a5a8cf760b11629815cdd18c111","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-09-12T15:25:52Z","title_canon_sha256":"f69178ff5d9376bf1934f0cb6654d5f161c83c9474d5f86ea7021855fe0b2e16"},"schema_version":"1.0","source":{"id":"1409.3769","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3769","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3769v3","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3769","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"T3ZJB7XMDR3S","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T3ZJB7XMDR3SNXVL","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T3ZJB7XM","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:bce8d76276f854178a271df4bced4d6efa81ea12c0def1350470802d28d19936","target":"graph","created_at":"2026-05-18T01:30:15Z","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":"We prove {\\rm (i)} Nichols algebra $\\mathfrak B(V)$ of vector space $V$ is finite-dimensional if and only if Nichols braided Lie algebra $\\mathfrak L(V)$ is finite-dimensional; {\\rm (ii)} If the rank of connected $V$ is $2$ and $\\mathfrak B(V)$ is an arithmetic root system, then $\\mathfrak B(V) = F \\oplus \\mathfrak L(V);$ and {\\rm (iii)} if $\\Delta (\\mathfrak B(V))$ is an arithmetic root system and there does not exist any $m$-infinity element with $p_{uu} \\not= 1$ for any $u \\in D(V)$, then $\\dim (\\mathfrak B(V) ) = \\infty$ if and only if there exists $V'$, which is twisting equivalent to $V$","authors_text":"Shouchuan Zhang, Weicai Wu, Yao-Zhong Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-09-12T15:25:52Z","title":"On Nichols (braided) Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3769","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:a0c551a6df5a62cf0d4b79446be6fbe2e4d2bd1bed71db2afe1ec7ee1ef5b0d7","target":"record","created_at":"2026-05-18T01:30:15Z","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":"1a0bfced03af7d26f57f3f53bfc9f1cdb4a54a5a8cf760b11629815cdd18c111","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-09-12T15:25:52Z","title_canon_sha256":"f69178ff5d9376bf1934f0cb6654d5f161c83c9474d5f86ea7021855fe0b2e16"},"schema_version":"1.0","source":{"id":"1409.3769","kind":"arxiv","version":3}},"canonical_sha256":"9ef290feec1c7726deab6be09f9dd0a253bbbfa16a8e85b3cdb720cf245f9977","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ef290feec1c7726deab6be09f9dd0a253bbbfa16a8e85b3cdb720cf245f9977","first_computed_at":"2026-05-18T01:30:15.487493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:15.487493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hRHH2sYfxRv8fFsXKbDTKQzCJ5w/+9NMyzCO/yOe4Nwek2DKhb8poTvr8rCzFP/5WyxIpyN59FcHXLbVMJddAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:15.488271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3769","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0c551a6df5a62cf0d4b79446be6fbe2e4d2bd1bed71db2afe1ec7ee1ef5b0d7","sha256:bce8d76276f854178a271df4bced4d6efa81ea12c0def1350470802d28d19936"],"state_sha256":"6f41f8b39a521687fe0e6d8b35615b5e74de2b88bbda9df4120d717afca9878a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ePFIeoG8NGQcPTEzA3anABkjoebqWtG+ZOInibp1KP747/aTMAM5pCC2ZlL4EMYkelMuaUwbK6C+Z3WPSxDMBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:16:23.204244Z","bundle_sha256":"4689a5e71b66a051636eaffc26e3f5fac88ec5840802c744acc35b5027aeea8e"}}