{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VU6BQPUG3KRN45QUZ6BA5HZDIU","short_pith_number":"pith:VU6BQPUG","canonical_record":{"source":{"id":"1710.02992","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-09T08:45:17Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"038ea756ce75e28da308012a108ab44fc4cced607c3072699415e71312156100","abstract_canon_sha256":"b98af879272d926dbb8ce9a4f4a5857cfceb9aae1e23c73eae22aa0e81f1d91a"},"schema_version":"1.0"},"canonical_sha256":"ad3c183e86daa2de7614cf820e9f23451aec6c62a59c2e586898065349e33103","source":{"kind":"arxiv","id":"1710.02992","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02992","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02992v1","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02992","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"VU6BQPUG3KRN","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VU6BQPUG3KRN45QU","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VU6BQPUG","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VU6BQPUG3KRN45QUZ6BA5HZDIU","target":"record","payload":{"canonical_record":{"source":{"id":"1710.02992","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-09T08:45:17Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"038ea756ce75e28da308012a108ab44fc4cced607c3072699415e71312156100","abstract_canon_sha256":"b98af879272d926dbb8ce9a4f4a5857cfceb9aae1e23c73eae22aa0e81f1d91a"},"schema_version":"1.0"},"canonical_sha256":"ad3c183e86daa2de7614cf820e9f23451aec6c62a59c2e586898065349e33103","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:00.086729Z","signature_b64":"JvoXu1aYdCrSX7+0YPsJdbqd6VonpIfB2QpVeveL/skXyGCkLpkgVOrW16CcLGtMQVtZflY38V2c8vtJlWnnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad3c183e86daa2de7614cf820e9f23451aec6c62a59c2e586898065349e33103","last_reissued_at":"2026-05-17T23:45:00.086215Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:00.086215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.02992","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":"2026-05-17T23:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"//f47MBX6vbizk663q5NDagKl8XN/0yGetIezA7VQLfX+TXw92jAuYZ6pwlciE36PUynxc4WUoHqb7bXBw9MAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:11:18.353940Z"},"content_sha256":"91f505b78cd3c849eb4c26427d6a4b1b5c3c5630566eac0e75c12695de251dad","schema_version":"1.0","event_id":"sha256:91f505b78cd3c849eb4c26427d6a4b1b5c3c5630566eac0e75c12695de251dad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VU6BQPUG3KRN45QUZ6BA5HZDIU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classifying spaces from Ore categories with Garside families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Stefan Witzel","submitted_at":"2017-10-09T08:45:17Z","abstract_excerpt":"We describe how an Ore category with a Garside family can be used to construct a classifying space for its fundamental group(s). The construction simultaneously generalizes Brady's classifying space for braid groups and the Stein--Farley complexes used for various relatives of Thompson's groups. It recovers the fact that Garside groups have finite classifying spaces.\n  We describe the categories and Garside structures underlying certain Thompson groups. The Zappa--Sz\\'ep product of categories is introduced and used to construct new categories and groups from known ones. As an illustration of o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02992","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":"2026-05-17T23:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pS/XO/2AumxUYb0+8KT6xgwFbeUVZDG728pEu97GX7eNlyW5kv46pLJbZlee/mxfJxwDmhHH5MEZb/b6HrRiCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:11:18.354283Z"},"content_sha256":"94c0a6e937b385e49065839a5b1d94b343572c1c74c29d77e9628aa7dbbac65a","schema_version":"1.0","event_id":"sha256:94c0a6e937b385e49065839a5b1d94b343572c1c74c29d77e9628aa7dbbac65a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VU6BQPUG3KRN45QUZ6BA5HZDIU/bundle.json","state_url":"https://pith.science/pith/VU6BQPUG3KRN45QUZ6BA5HZDIU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VU6BQPUG3KRN45QUZ6BA5HZDIU/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":"2026-05-31T05:11:18Z","links":{"resolver":"https://pith.science/pith/VU6BQPUG3KRN45QUZ6BA5HZDIU","bundle":"https://pith.science/pith/VU6BQPUG3KRN45QUZ6BA5HZDIU/bundle.json","state":"https://pith.science/pith/VU6BQPUG3KRN45QUZ6BA5HZDIU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VU6BQPUG3KRN45QUZ6BA5HZDIU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VU6BQPUG3KRN45QUZ6BA5HZDIU","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":"b98af879272d926dbb8ce9a4f4a5857cfceb9aae1e23c73eae22aa0e81f1d91a","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-09T08:45:17Z","title_canon_sha256":"038ea756ce75e28da308012a108ab44fc4cced607c3072699415e71312156100"},"schema_version":"1.0","source":{"id":"1710.02992","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02992","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02992v1","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02992","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"VU6BQPUG3KRN","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VU6BQPUG3KRN45QU","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VU6BQPUG","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:94c0a6e937b385e49065839a5b1d94b343572c1c74c29d77e9628aa7dbbac65a","target":"graph","created_at":"2026-05-17T23:45:00Z","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 describe how an Ore category with a Garside family can be used to construct a classifying space for its fundamental group(s). The construction simultaneously generalizes Brady's classifying space for braid groups and the Stein--Farley complexes used for various relatives of Thompson's groups. It recovers the fact that Garside groups have finite classifying spaces.\n  We describe the categories and Garside structures underlying certain Thompson groups. The Zappa--Sz\\'ep product of categories is introduced and used to construct new categories and groups from known ones. As an illustration of o","authors_text":"Stefan Witzel","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-09T08:45:17Z","title":"Classifying spaces from Ore categories with Garside families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02992","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":"sha256:91f505b78cd3c849eb4c26427d6a4b1b5c3c5630566eac0e75c12695de251dad","target":"record","created_at":"2026-05-17T23:45:00Z","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":"b98af879272d926dbb8ce9a4f4a5857cfceb9aae1e23c73eae22aa0e81f1d91a","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-09T08:45:17Z","title_canon_sha256":"038ea756ce75e28da308012a108ab44fc4cced607c3072699415e71312156100"},"schema_version":"1.0","source":{"id":"1710.02992","kind":"arxiv","version":1}},"canonical_sha256":"ad3c183e86daa2de7614cf820e9f23451aec6c62a59c2e586898065349e33103","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad3c183e86daa2de7614cf820e9f23451aec6c62a59c2e586898065349e33103","first_computed_at":"2026-05-17T23:45:00.086215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:00.086215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JvoXu1aYdCrSX7+0YPsJdbqd6VonpIfB2QpVeveL/skXyGCkLpkgVOrW16CcLGtMQVtZflY38V2c8vtJlWnnAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:00.086729Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.02992","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91f505b78cd3c849eb4c26427d6a4b1b5c3c5630566eac0e75c12695de251dad","sha256:94c0a6e937b385e49065839a5b1d94b343572c1c74c29d77e9628aa7dbbac65a"],"state_sha256":"eed47942d5e21585ce5ebe8b9668a577276bd35b6baf2bd8e4727634d50ebed6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0IKf07zkWPggCl8LzCe8AvZE9SMoOHU/JoyZhb0gbHIw2txqNAupOV00W+oGeEP3XALa/wtzVWqr+j+IPsWNAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:11:18.356654Z","bundle_sha256":"8f839ec39a6300f238bc41c97bde8d324957662ea55a6cae60d862f5587a4147"}}