{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6ZPHORFGBGZG35OZXQIYTMKMDG","short_pith_number":"pith:6ZPHORFG","canonical_record":{"source":{"id":"1609.03805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-09-13T12:50:13Z","cross_cats_sorted":["math.CT","math.KT","math.OA"],"title_canon_sha256":"efa151ea3e8147f236a7317655bf69606506e558a781e6a3a5a8329120c07b42","abstract_canon_sha256":"fe25cb93229f09515b40bce04e18ecd6ec3c36c9eebf39d9b74f4f66ac9daa21"},"schema_version":"1.0"},"canonical_sha256":"f65e7744a609b26df5d9bc1189b14c1984ed246c34f0ba08a1a23fea99d4c595","source":{"kind":"arxiv","id":"1609.03805","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03805","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03805v1","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03805","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"pith_short_12","alias_value":"6ZPHORFGBGZG","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6ZPHORFGBGZG35OZ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6ZPHORFG","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6ZPHORFGBGZG35OZXQIYTMKMDG","target":"record","payload":{"canonical_record":{"source":{"id":"1609.03805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-09-13T12:50:13Z","cross_cats_sorted":["math.CT","math.KT","math.OA"],"title_canon_sha256":"efa151ea3e8147f236a7317655bf69606506e558a781e6a3a5a8329120c07b42","abstract_canon_sha256":"fe25cb93229f09515b40bce04e18ecd6ec3c36c9eebf39d9b74f4f66ac9daa21"},"schema_version":"1.0"},"canonical_sha256":"f65e7744a609b26df5d9bc1189b14c1984ed246c34f0ba08a1a23fea99d4c595","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:57.221176Z","signature_b64":"owLFcujojOuWR6ZLNKgKPybrYtFYqlgTQ07gPnzcW0cfx8kYq6f7JS9CTuJlUI2P4m0OzcFNFiF9GkLtJ9w1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f65e7744a609b26df5d9bc1189b14c1984ed246c34f0ba08a1a23fea99d4c595","last_reissued_at":"2026-05-18T00:20:57.220528Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:57.220528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.03805","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":"2026-05-18T00:20:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EZJgpsRDwpYAQy48LlLzqAEUVMXJpbKMOutFRTjyBrGsiNVv3tl+yDKgyBdI0ss1YwnSZGvRE1KgEy9SD2ePBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:27:43.410778Z"},"content_sha256":"a0544b3cd9bf0f0e5d33b1b5ccb694719e110520107e95ec7fd7187bbdb6352e","schema_version":"1.0","event_id":"sha256:a0544b3cd9bf0f0e5d33b1b5ccb694719e110520107e95ec7fd7187bbdb6352e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6ZPHORFGBGZG35OZXQIYTMKMDG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Localization of Cofibration Categories and Groupoid $C^*$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.KT","math.OA"],"primary_cat":"math.AT","authors_text":"Karol Szumi{\\l}o, Markus Land, Thomas Nikolaus","submitted_at":"2016-09-13T12:50:13Z","abstract_excerpt":"We prove that relative functors out of a cofibration category are essentially the same as relative functors which are only defined on the subcategory of cofibrations. As an application we give a new construction of the functor that assigns to a groupoid its groupoid $C^*$-algebra and thereby its topological $K$-theory spectrum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03805","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":"2026-05-18T00:20:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gKdSWqsGX483P8bOOtZ4oJy4dI3uCRLzOdU6+huxVr1pCVMxGl2UW8cFNCaELqUyUWRGqNEYWol7GwZP4MVMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:27:43.411111Z"},"content_sha256":"2456ba5b2efe46c81b742c0267d1d07be6ad89f7049b5383273c0b7d012fe8ca","schema_version":"1.0","event_id":"sha256:2456ba5b2efe46c81b742c0267d1d07be6ad89f7049b5383273c0b7d012fe8ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ZPHORFGBGZG35OZXQIYTMKMDG/bundle.json","state_url":"https://pith.science/pith/6ZPHORFGBGZG35OZXQIYTMKMDG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ZPHORFGBGZG35OZXQIYTMKMDG/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":"2026-06-27T14:27:43Z","links":{"resolver":"https://pith.science/pith/6ZPHORFGBGZG35OZXQIYTMKMDG","bundle":"https://pith.science/pith/6ZPHORFGBGZG35OZXQIYTMKMDG/bundle.json","state":"https://pith.science/pith/6ZPHORFGBGZG35OZXQIYTMKMDG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ZPHORFGBGZG35OZXQIYTMKMDG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6ZPHORFGBGZG35OZXQIYTMKMDG","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":"fe25cb93229f09515b40bce04e18ecd6ec3c36c9eebf39d9b74f4f66ac9daa21","cross_cats_sorted":["math.CT","math.KT","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-09-13T12:50:13Z","title_canon_sha256":"efa151ea3e8147f236a7317655bf69606506e558a781e6a3a5a8329120c07b42"},"schema_version":"1.0","source":{"id":"1609.03805","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03805","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03805v1","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03805","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"pith_short_12","alias_value":"6ZPHORFGBGZG","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6ZPHORFGBGZG35OZ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6ZPHORFG","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:2456ba5b2efe46c81b742c0267d1d07be6ad89f7049b5383273c0b7d012fe8ca","target":"graph","created_at":"2026-05-18T00:20:57Z","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 prove that relative functors out of a cofibration category are essentially the same as relative functors which are only defined on the subcategory of cofibrations. As an application we give a new construction of the functor that assigns to a groupoid its groupoid $C^*$-algebra and thereby its topological $K$-theory spectrum.","authors_text":"Karol Szumi{\\l}o, Markus Land, Thomas Nikolaus","cross_cats":["math.CT","math.KT","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-09-13T12:50:13Z","title":"Localization of Cofibration Categories and Groupoid $C^*$-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03805","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:a0544b3cd9bf0f0e5d33b1b5ccb694719e110520107e95ec7fd7187bbdb6352e","target":"record","created_at":"2026-05-18T00:20:57Z","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":"fe25cb93229f09515b40bce04e18ecd6ec3c36c9eebf39d9b74f4f66ac9daa21","cross_cats_sorted":["math.CT","math.KT","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-09-13T12:50:13Z","title_canon_sha256":"efa151ea3e8147f236a7317655bf69606506e558a781e6a3a5a8329120c07b42"},"schema_version":"1.0","source":{"id":"1609.03805","kind":"arxiv","version":1}},"canonical_sha256":"f65e7744a609b26df5d9bc1189b14c1984ed246c34f0ba08a1a23fea99d4c595","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f65e7744a609b26df5d9bc1189b14c1984ed246c34f0ba08a1a23fea99d4c595","first_computed_at":"2026-05-18T00:20:57.220528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:57.220528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"owLFcujojOuWR6ZLNKgKPybrYtFYqlgTQ07gPnzcW0cfx8kYq6f7JS9CTuJlUI2P4m0OzcFNFiF9GkLtJ9w1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:57.221176Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03805","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0544b3cd9bf0f0e5d33b1b5ccb694719e110520107e95ec7fd7187bbdb6352e","sha256:2456ba5b2efe46c81b742c0267d1d07be6ad89f7049b5383273c0b7d012fe8ca"],"state_sha256":"087a9aabab1e0e24ef819cf928a8afe17bfc341172eb4d4feba1dfa40b652425"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ai9lzMMRodV2fPmwEx/QtjcjF7TUJMHxJ9YytzU0UdxpvpqouybLfyzGxgX3pgUkl/fQGkMGP/DGWdtqemqhDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T14:27:43.412931Z","bundle_sha256":"a53149de68875500269e3d325f02ef745c61077d5a9e077d317e8d00c5d59e52"}}