{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:JSMBMMK3QAYBJRPOXQNV4GIAUA","short_pith_number":"pith:JSMBMMK3","schema_version":"1.0","canonical_sha256":"4c9816315b803014c5eebc1b5e1900a01632a65b249b5cdda3f73128023eb01f","source":{"kind":"arxiv","id":"math/0212074","version":1},"attestation_state":"computed","paper":{"title":"The p-chain spectral sequence","license":"","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"James F. Davis, Wolfgang Lueck","submitted_at":"2002-12-05T00:53:50Z","abstract_excerpt":"We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah-Hirzebruch type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum-Connes and Farrell-Jones to compute algebraic K- and L-groups of group rings and topological K-groups of reduced group C*-algebras."},"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":"math/0212074","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2002-12-05T00:53:50Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"b2d87251a0a8de205a85ab7988c4c00352a24ebcd6f6df57e85b28a146e06c32","abstract_canon_sha256":"bc311ec418a21265e8468da670cd349b759df99b0872d7c1fde93aae8e479ce6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:48.060113Z","signature_b64":"+LXpz9fYUXtzYu9fK0fGxNtw05cwr9IgcdsoTwqjxh6695NTMeZI2LtNjWDx16BlQHuy4JKXOPTDl26pCK2FCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c9816315b803014c5eebc1b5e1900a01632a65b249b5cdda3f73128023eb01f","last_reissued_at":"2026-05-18T01:25:48.059626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:48.059626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The p-chain spectral sequence","license":"","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"James F. Davis, Wolfgang Lueck","submitted_at":"2002-12-05T00:53:50Z","abstract_excerpt":"We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah-Hirzebruch type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum-Connes and Farrell-Jones to compute algebraic K- and L-groups of group rings and topological K-groups of reduced group C*-algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0212074","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0212074","created_at":"2026-05-18T01:25:48.059689+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0212074v1","created_at":"2026-05-18T01:25:48.059689+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0212074","created_at":"2026-05-18T01:25:48.059689+00:00"},{"alias_kind":"pith_short_12","alias_value":"JSMBMMK3QAYB","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"JSMBMMK3QAYBJRPO","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"JSMBMMK3","created_at":"2026-05-18T12:25:50.845339+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/JSMBMMK3QAYBJRPOXQNV4GIAUA","json":"https://pith.science/pith/JSMBMMK3QAYBJRPOXQNV4GIAUA.json","graph_json":"https://pith.science/api/pith-number/JSMBMMK3QAYBJRPOXQNV4GIAUA/graph.json","events_json":"https://pith.science/api/pith-number/JSMBMMK3QAYBJRPOXQNV4GIAUA/events.json","paper":"https://pith.science/paper/JSMBMMK3"},"agent_actions":{"view_html":"https://pith.science/pith/JSMBMMK3QAYBJRPOXQNV4GIAUA","download_json":"https://pith.science/pith/JSMBMMK3QAYBJRPOXQNV4GIAUA.json","view_paper":"https://pith.science/paper/JSMBMMK3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0212074&json=true","fetch_graph":"https://pith.science/api/pith-number/JSMBMMK3QAYBJRPOXQNV4GIAUA/graph.json","fetch_events":"https://pith.science/api/pith-number/JSMBMMK3QAYBJRPOXQNV4GIAUA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JSMBMMK3QAYBJRPOXQNV4GIAUA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JSMBMMK3QAYBJRPOXQNV4GIAUA/action/storage_attestation","attest_author":"https://pith.science/pith/JSMBMMK3QAYBJRPOXQNV4GIAUA/action/author_attestation","sign_citation":"https://pith.science/pith/JSMBMMK3QAYBJRPOXQNV4GIAUA/action/citation_signature","submit_replication":"https://pith.science/pith/JSMBMMK3QAYBJRPOXQNV4GIAUA/action/replication_record"}},"created_at":"2026-05-18T01:25:48.059689+00:00","updated_at":"2026-05-18T01:25:48.059689+00:00"}