{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:Z2UEQTYYQHBNU7DK7YSEUGTDOP","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":"83bb8750fa3c20c05e71f35bba1c7bbdf9d8ed63c9d5a7c548f0dbe435502b8a","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2009-06-23T01:39:13Z","title_canon_sha256":"22ceff753afb094c260e3795bc99ae0d1335ff51af8d2103e0aa6f027ba6de84"},"schema_version":"1.0","source":{"id":"0906.4150","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.4150","created_at":"2026-05-18T02:24:55Z"},{"alias_kind":"arxiv_version","alias_value":"0906.4150v2","created_at":"2026-05-18T02:24:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.4150","created_at":"2026-05-18T02:24:55Z"},{"alias_kind":"pith_short_12","alias_value":"Z2UEQTYYQHBN","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"Z2UEQTYYQHBNU7DK","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"Z2UEQTYY","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:600f9c955e24e9814234d7bf48563c7158e4c76b248552fe69e954e27e0b7554","target":"graph","created_at":"2026-05-18T02:24:55Z","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":"In his 1973 paper Quillen proved a resolution theorem for the K-Theory of an exact category; his proof was homotopic in nature. By using the main result of a paper by Nenashev, we are able to give an algebraic proof of Quillen's Resolution Theorem for K_1 of an exact category.","authors_text":"Ben Whale","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2009-06-23T01:39:13Z","title":"An Algebraic Proof of Quillen's Resolution Theorem for K_1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.4150","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":"sha256:38683aa1fcfec5775aa5ea3be4c3bac8cc4e12e044ee0df26bdd4d55db6a2ff6","target":"record","created_at":"2026-05-18T02:24:55Z","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":"83bb8750fa3c20c05e71f35bba1c7bbdf9d8ed63c9d5a7c548f0dbe435502b8a","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2009-06-23T01:39:13Z","title_canon_sha256":"22ceff753afb094c260e3795bc99ae0d1335ff51af8d2103e0aa6f027ba6de84"},"schema_version":"1.0","source":{"id":"0906.4150","kind":"arxiv","version":2}},"canonical_sha256":"cea8484f1881c2da7c6afe244a1a6373e33427b4bbac628723ec60f1470e605b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cea8484f1881c2da7c6afe244a1a6373e33427b4bbac628723ec60f1470e605b","first_computed_at":"2026-05-18T02:24:55.407223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:55.407223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K1q3inMcQ92FkB+GsWIQR6QtzYdc+zgPkIrFjBKvBQ9cD1HUR77hA22Z2v4QWzlngI9MwGP4GsIVIDGGZKXcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:55.408186Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.4150","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38683aa1fcfec5775aa5ea3be4c3bac8cc4e12e044ee0df26bdd4d55db6a2ff6","sha256:600f9c955e24e9814234d7bf48563c7158e4c76b248552fe69e954e27e0b7554"],"state_sha256":"3b103bb45a8d104a3851b878ba3910e96240eccdf59fdecccfb769a13e19e343"}