{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M4JCAN32D52NKC467OUF6HF6IO","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":"618c7a24259de3c600a864efa7650e1a11164130b455a0ea5fb47085bb27b7fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-12-10T17:26:25Z","title_canon_sha256":"f27c41d4d08871f3628aade29c099ce229e2e8a58fb743ecf738f0243e80f45e"},"schema_version":"1.0","source":{"id":"1212.2143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2143","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2143v1","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2143","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"M4JCAN32D52N","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M4JCAN32D52NKC46","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M4JCAN32","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:c83429d4bf47355154d43590c644c3600b171e5bf731c9e78af4fb319479b129","target":"graph","created_at":"2026-05-18T03:38:46Z","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":"We give a streamlined proof of a theorem of Foxby and Halvorsen. The theorem states that certain relative K-groups made from chain complexes with bounded (but arbitrarily long) length coincide with similar K-groups in which one sets an absolute bound on the length of the complexes.","authors_text":"Daniel Dugger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-12-10T17:26:25Z","title":"Grothendieck groups of complexes with null-homotopies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2143","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":"sha256:43351702c9e66086ed649e2ecce2cf92e00457b48ec1231b8f992c108b522a03","target":"record","created_at":"2026-05-18T03:38:46Z","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":"618c7a24259de3c600a864efa7650e1a11164130b455a0ea5fb47085bb27b7fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-12-10T17:26:25Z","title_canon_sha256":"f27c41d4d08871f3628aade29c099ce229e2e8a58fb743ecf738f0243e80f45e"},"schema_version":"1.0","source":{"id":"1212.2143","kind":"arxiv","version":1}},"canonical_sha256":"671220377a1f74d50b9efba85f1cbe4399f69b845c17b12ace81acd45eebf226","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"671220377a1f74d50b9efba85f1cbe4399f69b845c17b12ace81acd45eebf226","first_computed_at":"2026-05-18T03:38:46.950087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:46.950087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AWXoYqarlf+SJ2xUHp9GOI3wNh+d66sTDLSBJZpvQvARrp7p+STJ4xnjx+sCvvyVH+GLUtzUHfPlM4nVV7aKDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:46.950778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.2143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43351702c9e66086ed649e2ecce2cf92e00457b48ec1231b8f992c108b522a03","sha256:c83429d4bf47355154d43590c644c3600b171e5bf731c9e78af4fb319479b129"],"state_sha256":"bfa7dc5811257f81f2c9d506b2e607542d812d24bf26ab85bfa20c52bba99bbf"}