{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QTUV7JTZF6A2MMFS4H3OUW63VS","short_pith_number":"pith:QTUV7JTZ","canonical_record":{"source":{"id":"1108.5157","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-08-25T18:54:49Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"68efee520638338bb9c6cd8fdccb2d8e5aa36560f9d2cc21968550aceae5cc29","abstract_canon_sha256":"8be1c970de1186a56f64c7a5ee6813c77e0f96e8716e08728e33e1792be66888"},"schema_version":"1.0"},"canonical_sha256":"84e95fa6792f81a630b2e1f6ea5bdbaca31de965d19ec349c848760fed5b3f77","source":{"kind":"arxiv","id":"1108.5157","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5157","created_at":"2026-05-18T04:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5157v2","created_at":"2026-05-18T04:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5157","created_at":"2026-05-18T04:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"QTUV7JTZF6A2","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QTUV7JTZF6A2MMFS","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QTUV7JTZ","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QTUV7JTZF6A2MMFS4H3OUW63VS","target":"record","payload":{"canonical_record":{"source":{"id":"1108.5157","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-08-25T18:54:49Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"68efee520638338bb9c6cd8fdccb2d8e5aa36560f9d2cc21968550aceae5cc29","abstract_canon_sha256":"8be1c970de1186a56f64c7a5ee6813c77e0f96e8716e08728e33e1792be66888"},"schema_version":"1.0"},"canonical_sha256":"84e95fa6792f81a630b2e1f6ea5bdbaca31de965d19ec349c848760fed5b3f77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:25.055077Z","signature_b64":"FCdyp5t6iMOwaA5jG13n3OkEEPTCAHfFcxRbq9CUw+QoSf6Wcy2pXmZPIK1+CiE7YOMWmqPy7fz7QM6YASLPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84e95fa6792f81a630b2e1f6ea5bdbaca31de965d19ec349c848760fed5b3f77","last_reissued_at":"2026-05-18T04:09:25.054480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:25.054480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.5157","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:09:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M5PbWruvACURJWRfS8VHco9+bjAk4c3qOOk1xtg1U0BAsc9boV2uLqmD4YnbbP9kkAUVunjFzRY3FFwB3o8KBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:07:42.680741Z"},"content_sha256":"094a9c53f710980b4dbd39a6b09df03444ca0541fcf32eb55373beabd689d92f","schema_version":"1.0","event_id":"sha256:094a9c53f710980b4dbd39a6b09df03444ca0541fcf32eb55373beabd689d92f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QTUV7JTZF6A2MMFS4H3OUW63VS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nichols algebras of unidentified diagonal type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Ivan Angiono","submitted_at":"2011-08-25T18:54:49Z","abstract_excerpt":"The Nichols algebras of diagonal type with finite root system are either of standard, super or (yet) unidentified type. A concrete description of the defining relations of all those Nichols algebras was given in \\cite{A-exp presentation}. In the present paper we use this result to give an explicit presentation of all Nichols algebras of unidentified type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5157","kind":"arxiv","version":2},"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":"2026-05-18T04:09:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YMr8ENZEh5QtE3sUDHke/rv+502Et9ul2IwwuGX8lPX8+jDjvKZNo3+YmQVzljVEcImOWFkqZQWbS/Z9fFEsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:07:42.681084Z"},"content_sha256":"1f110291728b7976b4c95b96405e8ff0f6deb13f073734ea8f921446e7baf2e7","schema_version":"1.0","event_id":"sha256:1f110291728b7976b4c95b96405e8ff0f6deb13f073734ea8f921446e7baf2e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QTUV7JTZF6A2MMFS4H3OUW63VS/bundle.json","state_url":"https://pith.science/pith/QTUV7JTZF6A2MMFS4H3OUW63VS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QTUV7JTZF6A2MMFS4H3OUW63VS/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":"2026-06-23T18:07:42Z","links":{"resolver":"https://pith.science/pith/QTUV7JTZF6A2MMFS4H3OUW63VS","bundle":"https://pith.science/pith/QTUV7JTZF6A2MMFS4H3OUW63VS/bundle.json","state":"https://pith.science/pith/QTUV7JTZF6A2MMFS4H3OUW63VS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QTUV7JTZF6A2MMFS4H3OUW63VS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QTUV7JTZF6A2MMFS4H3OUW63VS","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":"8be1c970de1186a56f64c7a5ee6813c77e0f96e8716e08728e33e1792be66888","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-08-25T18:54:49Z","title_canon_sha256":"68efee520638338bb9c6cd8fdccb2d8e5aa36560f9d2cc21968550aceae5cc29"},"schema_version":"1.0","source":{"id":"1108.5157","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5157","created_at":"2026-05-18T04:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5157v2","created_at":"2026-05-18T04:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5157","created_at":"2026-05-18T04:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"QTUV7JTZF6A2","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QTUV7JTZF6A2MMFS","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QTUV7JTZ","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:1f110291728b7976b4c95b96405e8ff0f6deb13f073734ea8f921446e7baf2e7","target":"graph","created_at":"2026-05-18T04:09:25Z","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":"The Nichols algebras of diagonal type with finite root system are either of standard, super or (yet) unidentified type. A concrete description of the defining relations of all those Nichols algebras was given in \\cite{A-exp presentation}. In the present paper we use this result to give an explicit presentation of all Nichols algebras of unidentified type.","authors_text":"Ivan Angiono","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-08-25T18:54:49Z","title":"Nichols algebras of unidentified diagonal type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5157","kind":"arxiv","version":2},"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":"sha256:094a9c53f710980b4dbd39a6b09df03444ca0541fcf32eb55373beabd689d92f","target":"record","created_at":"2026-05-18T04:09:25Z","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":"8be1c970de1186a56f64c7a5ee6813c77e0f96e8716e08728e33e1792be66888","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-08-25T18:54:49Z","title_canon_sha256":"68efee520638338bb9c6cd8fdccb2d8e5aa36560f9d2cc21968550aceae5cc29"},"schema_version":"1.0","source":{"id":"1108.5157","kind":"arxiv","version":2}},"canonical_sha256":"84e95fa6792f81a630b2e1f6ea5bdbaca31de965d19ec349c848760fed5b3f77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84e95fa6792f81a630b2e1f6ea5bdbaca31de965d19ec349c848760fed5b3f77","first_computed_at":"2026-05-18T04:09:25.054480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:25.054480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FCdyp5t6iMOwaA5jG13n3OkEEPTCAHfFcxRbq9CUw+QoSf6Wcy2pXmZPIK1+CiE7YOMWmqPy7fz7QM6YASLPBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:25.055077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5157","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:094a9c53f710980b4dbd39a6b09df03444ca0541fcf32eb55373beabd689d92f","sha256:1f110291728b7976b4c95b96405e8ff0f6deb13f073734ea8f921446e7baf2e7"],"state_sha256":"2f9dc2047ec0be502b01c0663f345d366f764350917aa22c361f2a6c9454c6ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NWhgoFa2WrwS8OZwkKw7d1lnDlzT9dSgH84jwWJ5xaRA6OupT+NugZFj+6gkQq4qQff5asT6VA6oCZE40ZPEBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:07:42.683072Z","bundle_sha256":"842444c44eff87928f1f2336ff6b4237d66f815d971b96306d51599df6a6e8cd"}}