{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JACFTTPFVQI3P36NZRJT6KDMOX","short_pith_number":"pith:JACFTTPF","schema_version":"1.0","canonical_sha256":"480459cde5ac11b7efcdcc533f286c75f6c83e2800344074af3c440e5c702f29","source":{"kind":"arxiv","id":"1310.8644","version":2},"attestation_state":"computed","paper":{"title":"Relative algebraic K-theory by elementary means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Daniel R. Grayson","submitted_at":"2013-10-31T19:09:39Z","abstract_excerpt":"In a previous paper I gave a presentation for the Quillen higher algebraic K-groups of an exact category in terms of \"acyclic binary multicomplexes\". In this paper I take that presentation as a definition of the higher K-groups, generalize it to the relative K-groups of an exact functor between exact categories, and produce the corresponding long exact sequence by elementary means, without homotopy theory."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.8644","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-10-31T19:09:39Z","cross_cats_sorted":[],"title_canon_sha256":"6ebe7254673c6de48dc8163f63454bc9b8b814c2b0d6966628f604c735436ef7","abstract_canon_sha256":"61a3f2702e50a7cf7db22949eb957fec173e3a59dd4c248077e30c86abb5e8e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:47.614244Z","signature_b64":"9DEigqj6zz8gxAH35bQCyEBtnVUYvYLkyVGLuTrepuJjP8AqNj2CbdXLcB42gpaBZVMKDBhVWHp+s+WzL2+6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"480459cde5ac11b7efcdcc533f286c75f6c83e2800344074af3c440e5c702f29","last_reissued_at":"2026-05-18T01:20:47.613792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:47.613792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative algebraic K-theory by elementary means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Daniel R. Grayson","submitted_at":"2013-10-31T19:09:39Z","abstract_excerpt":"In a previous paper I gave a presentation for the Quillen higher algebraic K-groups of an exact category in terms of \"acyclic binary multicomplexes\". In this paper I take that presentation as a definition of the higher K-groups, generalize it to the relative K-groups of an exact functor between exact categories, and produce the corresponding long exact sequence by elementary means, without homotopy theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8644","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1310.8644","created_at":"2026-05-18T01:20:47.613856+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.8644v2","created_at":"2026-05-18T01:20:47.613856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8644","created_at":"2026-05-18T01:20:47.613856+00:00"},{"alias_kind":"pith_short_12","alias_value":"JACFTTPFVQI3","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JACFTTPFVQI3P36N","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JACFTTPF","created_at":"2026-05-18T12:27:49.015174+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JACFTTPFVQI3P36NZRJT6KDMOX","json":"https://pith.science/pith/JACFTTPFVQI3P36NZRJT6KDMOX.json","graph_json":"https://pith.science/api/pith-number/JACFTTPFVQI3P36NZRJT6KDMOX/graph.json","events_json":"https://pith.science/api/pith-number/JACFTTPFVQI3P36NZRJT6KDMOX/events.json","paper":"https://pith.science/paper/JACFTTPF"},"agent_actions":{"view_html":"https://pith.science/pith/JACFTTPFVQI3P36NZRJT6KDMOX","download_json":"https://pith.science/pith/JACFTTPFVQI3P36NZRJT6KDMOX.json","view_paper":"https://pith.science/paper/JACFTTPF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.8644&json=true","fetch_graph":"https://pith.science/api/pith-number/JACFTTPFVQI3P36NZRJT6KDMOX/graph.json","fetch_events":"https://pith.science/api/pith-number/JACFTTPFVQI3P36NZRJT6KDMOX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JACFTTPFVQI3P36NZRJT6KDMOX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JACFTTPFVQI3P36NZRJT6KDMOX/action/storage_attestation","attest_author":"https://pith.science/pith/JACFTTPFVQI3P36NZRJT6KDMOX/action/author_attestation","sign_citation":"https://pith.science/pith/JACFTTPFVQI3P36NZRJT6KDMOX/action/citation_signature","submit_replication":"https://pith.science/pith/JACFTTPFVQI3P36NZRJT6KDMOX/action/replication_record"}},"created_at":"2026-05-18T01:20:47.613856+00:00","updated_at":"2026-05-18T01:20:47.613856+00:00"}