{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:44EMLUNF46XJ2DOAGXNPCIMZRA","short_pith_number":"pith:44EMLUNF","canonical_record":{"source":{"id":"2505.24555","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-05-30T13:05:46Z","cross_cats_sorted":["math.QA","math.RA"],"title_canon_sha256":"6a7d4f51f0a861df76b78d8ad69642331cebc3ec97af47d540e9a307088f7285","abstract_canon_sha256":"646c7ffd785d4bea6d2aba63147094e03f1388378924bd583c0082e88c48ae25"},"schema_version":"1.0"},"canonical_sha256":"e708c5d1a5e7ae9d0dc035daf12199880a4480a3386e4f4e1a2ff9ef765e97e0","source":{"kind":"arxiv","id":"2505.24555","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.24555","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"arxiv_version","alias_value":"2505.24555v1","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24555","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_12","alias_value":"44EMLUNF46XJ","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_16","alias_value":"44EMLUNF46XJ2DOA","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_8","alias_value":"44EMLUNF","created_at":"2026-07-05T11:12:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:44EMLUNF46XJ2DOAGXNPCIMZRA","target":"record","payload":{"canonical_record":{"source":{"id":"2505.24555","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-05-30T13:05:46Z","cross_cats_sorted":["math.QA","math.RA"],"title_canon_sha256":"6a7d4f51f0a861df76b78d8ad69642331cebc3ec97af47d540e9a307088f7285","abstract_canon_sha256":"646c7ffd785d4bea6d2aba63147094e03f1388378924bd583c0082e88c48ae25"},"schema_version":"1.0"},"canonical_sha256":"e708c5d1a5e7ae9d0dc035daf12199880a4480a3386e4f4e1a2ff9ef765e97e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:12:52.206937Z","signature_b64":"bTUfizCUbJdOfjdnxnPAY1n2/i+HZCfLdFXa3Z1LbLYsvAqAZJ1ON4ZXZ7+9IrnIL3D/SXm4wEe43pnyhmi2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e708c5d1a5e7ae9d0dc035daf12199880a4480a3386e4f4e1a2ff9ef765e97e0","last_reissued_at":"2026-07-05T11:12:52.206351Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:12:52.206351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.24555","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":"2026-07-05T11:12:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U/qYLYUWo4NRn9suA6q0Z07NkNHUJiGpFd42MfRKvCFtsWFyhKhrEExTTN9Qsbk4G6Cr7POcDW4HvNIOk+pYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T01:10:05.152888Z"},"content_sha256":"c7b2fca48cedffdb58074fadc4130cf8ace1589c5224a7d71d29fbf6571f0f2b","schema_version":"1.0","event_id":"sha256:c7b2fca48cedffdb58074fadc4130cf8ace1589c5224a7d71d29fbf6571f0f2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:44EMLUNF46XJ2DOAGXNPCIMZRA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing finite Weyl groupoids","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Iv\\'an Angiono, Leandro Vendramin","submitted_at":"2025-05-30T13:05:46Z","abstract_excerpt":"We present algorithms to compute generalized root systems of Nichols algebras of diagonal type and of contragredient Lie superalgebras. As a consequence, we obtain an algorithm to compute the Lyndon words in the Kharchenko PBW basis associated to each positive root, along with their corresponding hyperwords. This data is essential for obtaining a minimal presentation of Nichols algebras of diagonal type with a finite root system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24555","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.24555/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:12:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IEfRTnlepF0PDyIUpn/vdHYQ+F50ekPJewNngLH7PyNf9uRyLuuMGVZAGUkT3TK4rqUJpfWib4Vuhb3lMx+KDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T01:10:05.153396Z"},"content_sha256":"fad6c59f04bdb72c581a42476e8f48fed876f5c962d12760727210e80d786a4e","schema_version":"1.0","event_id":"sha256:fad6c59f04bdb72c581a42476e8f48fed876f5c962d12760727210e80d786a4e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/44EMLUNF46XJ2DOAGXNPCIMZRA/bundle.json","state_url":"https://pith.science/pith/44EMLUNF46XJ2DOAGXNPCIMZRA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/44EMLUNF46XJ2DOAGXNPCIMZRA/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":"2026-08-08T01:10:05Z","links":{"resolver":"https://pith.science/pith/44EMLUNF46XJ2DOAGXNPCIMZRA","bundle":"https://pith.science/pith/44EMLUNF46XJ2DOAGXNPCIMZRA/bundle.json","state":"https://pith.science/pith/44EMLUNF46XJ2DOAGXNPCIMZRA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/44EMLUNF46XJ2DOAGXNPCIMZRA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:44EMLUNF46XJ2DOAGXNPCIMZRA","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":"646c7ffd785d4bea6d2aba63147094e03f1388378924bd583c0082e88c48ae25","cross_cats_sorted":["math.QA","math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-05-30T13:05:46Z","title_canon_sha256":"6a7d4f51f0a861df76b78d8ad69642331cebc3ec97af47d540e9a307088f7285"},"schema_version":"1.0","source":{"id":"2505.24555","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.24555","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"arxiv_version","alias_value":"2505.24555v1","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24555","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_12","alias_value":"44EMLUNF46XJ","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_16","alias_value":"44EMLUNF46XJ2DOA","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_8","alias_value":"44EMLUNF","created_at":"2026-07-05T11:12:52Z"}],"graph_snapshots":[{"event_id":"sha256:fad6c59f04bdb72c581a42476e8f48fed876f5c962d12760727210e80d786a4e","target":"graph","created_at":"2026-07-05T11:12:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.24555/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present algorithms to compute generalized root systems of Nichols algebras of diagonal type and of contragredient Lie superalgebras. As a consequence, we obtain an algorithm to compute the Lyndon words in the Kharchenko PBW basis associated to each positive root, along with their corresponding hyperwords. This data is essential for obtaining a minimal presentation of Nichols algebras of diagonal type with a finite root system.","authors_text":"Iv\\'an Angiono, Leandro Vendramin","cross_cats":["math.QA","math.RA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-05-30T13:05:46Z","title":"Computing finite Weyl groupoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24555","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:c7b2fca48cedffdb58074fadc4130cf8ace1589c5224a7d71d29fbf6571f0f2b","target":"record","created_at":"2026-07-05T11:12:52Z","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":"646c7ffd785d4bea6d2aba63147094e03f1388378924bd583c0082e88c48ae25","cross_cats_sorted":["math.QA","math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-05-30T13:05:46Z","title_canon_sha256":"6a7d4f51f0a861df76b78d8ad69642331cebc3ec97af47d540e9a307088f7285"},"schema_version":"1.0","source":{"id":"2505.24555","kind":"arxiv","version":1}},"canonical_sha256":"e708c5d1a5e7ae9d0dc035daf12199880a4480a3386e4f4e1a2ff9ef765e97e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e708c5d1a5e7ae9d0dc035daf12199880a4480a3386e4f4e1a2ff9ef765e97e0","first_computed_at":"2026-07-05T11:12:52.206351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:12:52.206351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bTUfizCUbJdOfjdnxnPAY1n2/i+HZCfLdFXa3Z1LbLYsvAqAZJ1ON4ZXZ7+9IrnIL3D/SXm4wEe43pnyhmi2Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:12:52.206937Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.24555","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7b2fca48cedffdb58074fadc4130cf8ace1589c5224a7d71d29fbf6571f0f2b","sha256:fad6c59f04bdb72c581a42476e8f48fed876f5c962d12760727210e80d786a4e"],"state_sha256":"340038edafb634ae5f31479bcc38824684f7f83c6fb5151cdf3da97bbedea970"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ygYwzUc2n2YyPI2McmTmZ9bkHbDvZtYPDlIt00X50MMjGQmNlHYG+wNPKYEIhULRVENOMu1K5AIgo0bq9cwpBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T01:10:05.160036Z","bundle_sha256":"e8cb514661fc4586a1fc69b2935d10717b0d9651840135239fd36b10d91c3e9a"}}