{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GXQ55Y4PNOKS3ZPZLL3RRUFN75","short_pith_number":"pith:GXQ55Y4P","canonical_record":{"source":{"id":"1210.5423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-19T14:00:23Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"ba8af3a8779927d758b9a7a4800e3cd4d7c46d2b01e734cfe89d43e3ea372555","abstract_canon_sha256":"7392011227579ebaf34d92526b71052c8e261780a841cfbde19b076e35664730"},"schema_version":"1.0"},"canonical_sha256":"35e1dee38f6b952de5f95af718d0adff7dea293d46acfde4522e5d82100fe77c","source":{"kind":"arxiv","id":"1210.5423","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5423","created_at":"2026-05-18T03:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5423v1","created_at":"2026-05-18T03:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5423","created_at":"2026-05-18T03:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"GXQ55Y4PNOKS","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GXQ55Y4PNOKS3ZPZ","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GXQ55Y4P","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GXQ55Y4PNOKS3ZPZLL3RRUFN75","target":"record","payload":{"canonical_record":{"source":{"id":"1210.5423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-19T14:00:23Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"ba8af3a8779927d758b9a7a4800e3cd4d7c46d2b01e734cfe89d43e3ea372555","abstract_canon_sha256":"7392011227579ebaf34d92526b71052c8e261780a841cfbde19b076e35664730"},"schema_version":"1.0"},"canonical_sha256":"35e1dee38f6b952de5f95af718d0adff7dea293d46acfde4522e5d82100fe77c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:46.463888Z","signature_b64":"5/eRZiHW745H12NO3YDBVW7IsxqIhaTTgQatk83fubmUQ0OVltPc8L+DqPx+njNgIrEwvxZFUhBtDgbbiO0sBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35e1dee38f6b952de5f95af718d0adff7dea293d46acfde4522e5d82100fe77c","last_reissued_at":"2026-05-18T03:12:46.463190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:46.463190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.5423","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":"2026-05-18T03:12:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a8nbk4KmerwsV0kZNiHFn4yS+0r2OamykjsqnP6L8UACIeWdt63ihYXuE14cXFfjRs7BNls7T5e8hnzYzhuoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:41:37.936267Z"},"content_sha256":"bcaccc22a161e4826caa66093f7b01c855a600fc9f199df7398bbc227ba83822","schema_version":"1.0","event_id":"sha256:bcaccc22a161e4826caa66093f7b01c855a600fc9f199df7398bbc227ba83822"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GXQ55Y4PNOKS3ZPZLL3RRUFN75","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fomin-Kirillov algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Leandro Vendramin","submitted_at":"2012-10-19T14:00:23Z","abstract_excerpt":"This is an extended abstract of the talk given in the Oberwolfach miniworkshop \"Nichols algebras and Weyl groupoids\" in October 2012."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5423","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":"2026-05-18T03:12:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qhp2kc97W/FqrHIQkaKsVk4HmEoUPB9i4h8C8zDFwBFY94zHM1TUBosAACO13Z8TRllgbji9HtsDQ1EuLjUVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:41:37.936647Z"},"content_sha256":"cd36b296a117fa52f97c6b2b957c31f00a57bedb5e5780d7e2aec75a0f7014d4","schema_version":"1.0","event_id":"sha256:cd36b296a117fa52f97c6b2b957c31f00a57bedb5e5780d7e2aec75a0f7014d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GXQ55Y4PNOKS3ZPZLL3RRUFN75/bundle.json","state_url":"https://pith.science/pith/GXQ55Y4PNOKS3ZPZLL3RRUFN75/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GXQ55Y4PNOKS3ZPZLL3RRUFN75/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":"2026-06-22T23:41:37Z","links":{"resolver":"https://pith.science/pith/GXQ55Y4PNOKS3ZPZLL3RRUFN75","bundle":"https://pith.science/pith/GXQ55Y4PNOKS3ZPZLL3RRUFN75/bundle.json","state":"https://pith.science/pith/GXQ55Y4PNOKS3ZPZLL3RRUFN75/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GXQ55Y4PNOKS3ZPZLL3RRUFN75/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GXQ55Y4PNOKS3ZPZLL3RRUFN75","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":"7392011227579ebaf34d92526b71052c8e261780a841cfbde19b076e35664730","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-19T14:00:23Z","title_canon_sha256":"ba8af3a8779927d758b9a7a4800e3cd4d7c46d2b01e734cfe89d43e3ea372555"},"schema_version":"1.0","source":{"id":"1210.5423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5423","created_at":"2026-05-18T03:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5423v1","created_at":"2026-05-18T03:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5423","created_at":"2026-05-18T03:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"GXQ55Y4PNOKS","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GXQ55Y4PNOKS3ZPZ","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GXQ55Y4P","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:cd36b296a117fa52f97c6b2b957c31f00a57bedb5e5780d7e2aec75a0f7014d4","target":"graph","created_at":"2026-05-18T03:12:46Z","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":"This is an extended abstract of the talk given in the Oberwolfach miniworkshop \"Nichols algebras and Weyl groupoids\" in October 2012.","authors_text":"Leandro Vendramin","cross_cats":["math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-19T14:00:23Z","title":"Fomin-Kirillov algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5423","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:bcaccc22a161e4826caa66093f7b01c855a600fc9f199df7398bbc227ba83822","target":"record","created_at":"2026-05-18T03:12:46Z","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":"7392011227579ebaf34d92526b71052c8e261780a841cfbde19b076e35664730","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-19T14:00:23Z","title_canon_sha256":"ba8af3a8779927d758b9a7a4800e3cd4d7c46d2b01e734cfe89d43e3ea372555"},"schema_version":"1.0","source":{"id":"1210.5423","kind":"arxiv","version":1}},"canonical_sha256":"35e1dee38f6b952de5f95af718d0adff7dea293d46acfde4522e5d82100fe77c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35e1dee38f6b952de5f95af718d0adff7dea293d46acfde4522e5d82100fe77c","first_computed_at":"2026-05-18T03:12:46.463190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:46.463190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5/eRZiHW745H12NO3YDBVW7IsxqIhaTTgQatk83fubmUQ0OVltPc8L+DqPx+njNgIrEwvxZFUhBtDgbbiO0sBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:46.463888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcaccc22a161e4826caa66093f7b01c855a600fc9f199df7398bbc227ba83822","sha256:cd36b296a117fa52f97c6b2b957c31f00a57bedb5e5780d7e2aec75a0f7014d4"],"state_sha256":"7cc0e2a106cafb2b0b86cf8307ec6f5800ebc5039a67a3bf41143b173c8f9f82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wMoKAh0rpcx4Qlp//OeVnZSHaZTvjMedztDJssvNitPbu72+23ebuu4MtPxNH3F5bZOWlyVBWm0YzdtfFY2RCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:41:37.938543Z","bundle_sha256":"2275f53b7e8c8e1b96cd7d94069c5f80469605ecca715686c90b2e592b14208a"}}