{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:6EB5JE7K5EMNVLEUH6VHSEJTS4","short_pith_number":"pith:6EB5JE7K","canonical_record":{"source":{"id":"1008.4144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-08-24T20:30:01Z","cross_cats_sorted":[],"title_canon_sha256":"95800cc66d6cc1bf3c5ca6abdb450d934bd4e5bef8280e5e1f1d6281291b18d8","abstract_canon_sha256":"82db1ce91c80df78363cd97f41805a799c78ea19d41f16d42df9521c589614e9"},"schema_version":"1.0"},"canonical_sha256":"f103d493eae918daac943faa7911339736fafbbae3812aa881b01786fbe06374","source":{"kind":"arxiv","id":"1008.4144","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4144","created_at":"2026-05-18T04:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4144v1","created_at":"2026-05-18T04:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4144","created_at":"2026-05-18T04:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"6EB5JE7K5EMN","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6EB5JE7K5EMNVLEU","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6EB5JE7K","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:6EB5JE7K5EMNVLEUH6VHSEJTS4","target":"record","payload":{"canonical_record":{"source":{"id":"1008.4144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-08-24T20:30:01Z","cross_cats_sorted":[],"title_canon_sha256":"95800cc66d6cc1bf3c5ca6abdb450d934bd4e5bef8280e5e1f1d6281291b18d8","abstract_canon_sha256":"82db1ce91c80df78363cd97f41805a799c78ea19d41f16d42df9521c589614e9"},"schema_version":"1.0"},"canonical_sha256":"f103d493eae918daac943faa7911339736fafbbae3812aa881b01786fbe06374","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:53.617459Z","signature_b64":"bNAuRpfbZ4ruG2s/wpLrjeDkmVhVloyd0zdeFpj1MeRjeZ6b2ck+ajT/L2iqmkalOZHHfckgUk/es8A7BAWQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f103d493eae918daac943faa7911339736fafbbae3812aa881b01786fbe06374","last_reissued_at":"2026-05-18T04:41:53.616913Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:53.616913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.4144","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":"2026-05-18T04:41:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vhobaaPAwB6pWaEI4yk+7qvCV/goPOconl4To0EuxhcGn52QsuxJe/Go5JOoPgP4gQFdVpj3Tu7VfMQfOeusDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:52:30.130757Z"},"content_sha256":"431a32d7d13817f6aa4d3ce57f43dfd8e65a9ac3e67c61d5589954d719731a95","schema_version":"1.0","event_id":"sha256:431a32d7d13817f6aa4d3ce57f43dfd8e65a9ac3e67c61d5589954d719731a95"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:6EB5JE7K5EMNVLEUH6VHSEJTS4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Iv\\'an Ezequiel Angiono","submitted_at":"2010-08-24T20:30:01Z","abstract_excerpt":"We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based in Kharchenko's theory of PBW basis of Lyndon words. We prove that the lexicographic order on Lyndon words is convex for such PBW generators and so the PBW basis is orthogonal with respect to the canonical non-degenerate form associated to the Nichols algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4144","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":"2026-05-18T04:41:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bc1eyHT3iOL8tWgt+e54ocEErTi+IEpbpG0IY7OHGcYosOAgKMsX3l9nttjnN90ybSsM/PLnMTfwx/eVvJTTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:52:30.131104Z"},"content_sha256":"8ddc68e0f09b7d74bc487e73848f96d60cab43235ed2b5d71b084c67e533a2b8","schema_version":"1.0","event_id":"sha256:8ddc68e0f09b7d74bc487e73848f96d60cab43235ed2b5d71b084c67e533a2b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6EB5JE7K5EMNVLEUH6VHSEJTS4/bundle.json","state_url":"https://pith.science/pith/6EB5JE7K5EMNVLEUH6VHSEJTS4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6EB5JE7K5EMNVLEUH6VHSEJTS4/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":"2026-06-24T06:52:30Z","links":{"resolver":"https://pith.science/pith/6EB5JE7K5EMNVLEUH6VHSEJTS4","bundle":"https://pith.science/pith/6EB5JE7K5EMNVLEUH6VHSEJTS4/bundle.json","state":"https://pith.science/pith/6EB5JE7K5EMNVLEUH6VHSEJTS4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6EB5JE7K5EMNVLEUH6VHSEJTS4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6EB5JE7K5EMNVLEUH6VHSEJTS4","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":"82db1ce91c80df78363cd97f41805a799c78ea19d41f16d42df9521c589614e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-08-24T20:30:01Z","title_canon_sha256":"95800cc66d6cc1bf3c5ca6abdb450d934bd4e5bef8280e5e1f1d6281291b18d8"},"schema_version":"1.0","source":{"id":"1008.4144","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4144","created_at":"2026-05-18T04:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4144v1","created_at":"2026-05-18T04:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4144","created_at":"2026-05-18T04:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"6EB5JE7K5EMN","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6EB5JE7K5EMNVLEU","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6EB5JE7K","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:8ddc68e0f09b7d74bc487e73848f96d60cab43235ed2b5d71b084c67e533a2b8","target":"graph","created_at":"2026-05-18T04:41:53Z","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 obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based in Kharchenko's theory of PBW basis of Lyndon words. We prove that the lexicographic order on Lyndon words is convex for such PBW generators and so the PBW basis is orthogonal with respect to the canonical non-degenerate form associated to the Nichols algebra.","authors_text":"Iv\\'an Ezequiel Angiono","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-08-24T20:30:01Z","title":"A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4144","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":"sha256:431a32d7d13817f6aa4d3ce57f43dfd8e65a9ac3e67c61d5589954d719731a95","target":"record","created_at":"2026-05-18T04:41:53Z","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":"82db1ce91c80df78363cd97f41805a799c78ea19d41f16d42df9521c589614e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-08-24T20:30:01Z","title_canon_sha256":"95800cc66d6cc1bf3c5ca6abdb450d934bd4e5bef8280e5e1f1d6281291b18d8"},"schema_version":"1.0","source":{"id":"1008.4144","kind":"arxiv","version":1}},"canonical_sha256":"f103d493eae918daac943faa7911339736fafbbae3812aa881b01786fbe06374","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f103d493eae918daac943faa7911339736fafbbae3812aa881b01786fbe06374","first_computed_at":"2026-05-18T04:41:53.616913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:53.616913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bNAuRpfbZ4ruG2s/wpLrjeDkmVhVloyd0zdeFpj1MeRjeZ6b2ck+ajT/L2iqmkalOZHHfckgUk/es8A7BAWQAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:53.617459Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.4144","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:431a32d7d13817f6aa4d3ce57f43dfd8e65a9ac3e67c61d5589954d719731a95","sha256:8ddc68e0f09b7d74bc487e73848f96d60cab43235ed2b5d71b084c67e533a2b8"],"state_sha256":"016cfa2737899c04278ad9cb1d04102dafd27d144d9db41d391f6f11ba00a53a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SaRkOB1a9Rue3mWBD99vY+L0mZvYOmEchAvjH83bt2Jinz2NeW5iX3+7BnTD1lwBnP0Z0Qh/aUXjMNM+ekztAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:52:30.133087Z","bundle_sha256":"869762285d533592cf2f280d75cec68d651141394c70cda845f85ce8bb30ca97"}}