{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:67NBLXO4JLRYGP5ZGLHSX6ODRZ","short_pith_number":"pith:67NBLXO4","canonical_record":{"source":{"id":"1012.2824","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-13T18:29:11Z","cross_cats_sorted":[],"title_canon_sha256":"10c6555773b4930b15cb1a75fc9b79df555a5ffb175b4781a60c02e6cd9c6673","abstract_canon_sha256":"d69cb63834f5e31a6a854f0f8d2a4311eb6698aa0cc5e5e1a886620ca1dcde12"},"schema_version":"1.0"},"canonical_sha256":"f7da15dddc4ae3833fb932cf2bf9c38e6ac1852aa4f61c307648747b3ee307aa","source":{"kind":"arxiv","id":"1012.2824","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2824","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2824v4","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2824","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"pith_short_12","alias_value":"67NBLXO4JLRY","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"67NBLXO4JLRYGP5Z","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"67NBLXO4","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:67NBLXO4JLRYGP5ZGLHSX6ODRZ","target":"record","payload":{"canonical_record":{"source":{"id":"1012.2824","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-13T18:29:11Z","cross_cats_sorted":[],"title_canon_sha256":"10c6555773b4930b15cb1a75fc9b79df555a5ffb175b4781a60c02e6cd9c6673","abstract_canon_sha256":"d69cb63834f5e31a6a854f0f8d2a4311eb6698aa0cc5e5e1a886620ca1dcde12"},"schema_version":"1.0"},"canonical_sha256":"f7da15dddc4ae3833fb932cf2bf9c38e6ac1852aa4f61c307648747b3ee307aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:29.113230Z","signature_b64":"+y86BZTYO/pKnLJUdqCcSJBgoLu/6FbP+JOozBoAqmMv/OfuqAx4IHVGNMCvD2gWJapnt0UP32U3ktxU1clWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7da15dddc4ae3833fb932cf2bf9c38e6ac1852aa4f61c307648747b3ee307aa","last_reissued_at":"2026-05-18T00:48:29.112747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:29.112747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.2824","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZXXiNJcatJ5xMUmmBwpvn9PzxE03UuTrgERhtWhDmtidQ/bc3BG1OiK79qamBxbVdy6FjVoun9kovybms8j8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:40:21.951310Z"},"content_sha256":"2e7eefaa49e2653c5d0627b4498eca1193dd557de226a64f5803c8a4b5e845a3","schema_version":"1.0","event_id":"sha256:2e7eefaa49e2653c5d0627b4498eca1193dd557de226a64f5803c8a4b5e845a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:67NBLXO4JLRYGP5ZGLHSX6ODRZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Covering morphisms of groupoids, derived modules and a 1-dimensional Relative Hurewicz Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ronald Brown","submitted_at":"2010-12-13T18:29:11Z","abstract_excerpt":"We fill a lacuna in the literature by giving a version in dimension 1 of the Relative Hurewicz Theorem, and relate this to abelianisations of groupoids, covering spaces and covering morphisms of groupoids, and Crowell's notion of derived modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2824","kind":"arxiv","version":4},"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":"2026-05-18T00:48:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qlif76eHx11nwcphkRUdHDqQP4XSgTtigpEX3TpoG9fEhaC8sF5u83YGOdC2d5oWJRMjVWepybAvQxNbyp+iAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:40:21.951674Z"},"content_sha256":"8873495660b1db89bfb5a33ea3a0554a5a69094df3e5ebaa842d6c397abe3e81","schema_version":"1.0","event_id":"sha256:8873495660b1db89bfb5a33ea3a0554a5a69094df3e5ebaa842d6c397abe3e81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/67NBLXO4JLRYGP5ZGLHSX6ODRZ/bundle.json","state_url":"https://pith.science/pith/67NBLXO4JLRYGP5ZGLHSX6ODRZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/67NBLXO4JLRYGP5ZGLHSX6ODRZ/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":"2026-06-24T22:40:21Z","links":{"resolver":"https://pith.science/pith/67NBLXO4JLRYGP5ZGLHSX6ODRZ","bundle":"https://pith.science/pith/67NBLXO4JLRYGP5ZGLHSX6ODRZ/bundle.json","state":"https://pith.science/pith/67NBLXO4JLRYGP5ZGLHSX6ODRZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/67NBLXO4JLRYGP5ZGLHSX6ODRZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:67NBLXO4JLRYGP5ZGLHSX6ODRZ","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":"d69cb63834f5e31a6a854f0f8d2a4311eb6698aa0cc5e5e1a886620ca1dcde12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-13T18:29:11Z","title_canon_sha256":"10c6555773b4930b15cb1a75fc9b79df555a5ffb175b4781a60c02e6cd9c6673"},"schema_version":"1.0","source":{"id":"1012.2824","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2824","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2824v4","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2824","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"pith_short_12","alias_value":"67NBLXO4JLRY","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"67NBLXO4JLRYGP5Z","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"67NBLXO4","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:8873495660b1db89bfb5a33ea3a0554a5a69094df3e5ebaa842d6c397abe3e81","target":"graph","created_at":"2026-05-18T00:48:29Z","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 fill a lacuna in the literature by giving a version in dimension 1 of the Relative Hurewicz Theorem, and relate this to abelianisations of groupoids, covering spaces and covering morphisms of groupoids, and Crowell's notion of derived modules.","authors_text":"Ronald Brown","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-13T18:29:11Z","title":"Covering morphisms of groupoids, derived modules and a 1-dimensional Relative Hurewicz Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2824","kind":"arxiv","version":4},"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":"sha256:2e7eefaa49e2653c5d0627b4498eca1193dd557de226a64f5803c8a4b5e845a3","target":"record","created_at":"2026-05-18T00:48:29Z","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":"d69cb63834f5e31a6a854f0f8d2a4311eb6698aa0cc5e5e1a886620ca1dcde12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-13T18:29:11Z","title_canon_sha256":"10c6555773b4930b15cb1a75fc9b79df555a5ffb175b4781a60c02e6cd9c6673"},"schema_version":"1.0","source":{"id":"1012.2824","kind":"arxiv","version":4}},"canonical_sha256":"f7da15dddc4ae3833fb932cf2bf9c38e6ac1852aa4f61c307648747b3ee307aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7da15dddc4ae3833fb932cf2bf9c38e6ac1852aa4f61c307648747b3ee307aa","first_computed_at":"2026-05-18T00:48:29.112747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:29.112747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+y86BZTYO/pKnLJUdqCcSJBgoLu/6FbP+JOozBoAqmMv/OfuqAx4IHVGNMCvD2gWJapnt0UP32U3ktxU1clWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:29.113230Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2824","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e7eefaa49e2653c5d0627b4498eca1193dd557de226a64f5803c8a4b5e845a3","sha256:8873495660b1db89bfb5a33ea3a0554a5a69094df3e5ebaa842d6c397abe3e81"],"state_sha256":"07d8fcf29cddaf3a6f225490ac7e73e961a321e9e0c9070a42fa594d9b6a6ce6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+c2mc1U8KSDjg187w4wDojx+MVuFXJbX8+k7HqAVRptuEb468+hzvsOu9jSxMrt87RB4ZHG+vGA06oV55vV8Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:40:21.953664Z","bundle_sha256":"e1891852d5e160f05e33e707108aff0728ef268aa9e87f2dca2aaaff42b83179"}}