{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:CMKUOGZ5FCFCP3AA3HKUJ3UXBR","short_pith_number":"pith:CMKUOGZ5","schema_version":"1.0","canonical_sha256":"1315471b3d288a27ec00d9d544ee970c6919da253f25c825b07d64bbbdf13fd7","source":{"kind":"arxiv","id":"2207.14629","version":1},"attestation_state":"computed","paper":{"title":"Finite domination and Novikov homology over strongly $\\mathbb{Z}^2$-graded rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AT","math.RA"],"primary_cat":"math.KT","authors_text":"Luke Steers, Thomas Huettemann","submitted_at":"2022-07-29T12:12:43Z","abstract_excerpt":"Let $R$ be a strongly $\\mathbb{Z}^2$-graded ring, and let $C$ be a bounded chain complex of finitely generated free $R$-modules. The complex $C$ is $R_{(0,0)}$-finitely dominated, or of type FP over $R_{(0,0)}$, if it is chain homotopy equivalent to a bounded complex of finitely generated projective $R_{(0,0)}$-modules. We show that this happens if and only if $C$ becomes acyclic after taking tensor product with a certain eight rings of formal power series, the graded analogues of classical Novikov rings. This extends results of Ranicki, Quinn and the first author on Laurent polynomial rings i"},"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":"2207.14629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2022-07-29T12:12:43Z","cross_cats_sorted":["math.AC","math.AT","math.RA"],"title_canon_sha256":"30fb8911596016117f117b9dc32822d338e08efb1e00642b6455599541e2aca7","abstract_canon_sha256":"8ac7474aa6d5c0466fc72560ed611009fd380b1f86baa1139a137047909ca95c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T02:04:44.730381Z","signature_b64":"yLquue17oGvMdQSWgW/KH8cOVSmOA2ZGR3zboa3cJakuiXdDvPZHzCqWbE+zN+i+u5k3pIk7XOfX4h/OJTfUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1315471b3d288a27ec00d9d544ee970c6919da253f25c825b07d64bbbdf13fd7","last_reissued_at":"2026-05-21T02:04:44.729538Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T02:04:44.729538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite domination and Novikov homology over strongly $\\mathbb{Z}^2$-graded rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AT","math.RA"],"primary_cat":"math.KT","authors_text":"Luke Steers, Thomas Huettemann","submitted_at":"2022-07-29T12:12:43Z","abstract_excerpt":"Let $R$ be a strongly $\\mathbb{Z}^2$-graded ring, and let $C$ be a bounded chain complex of finitely generated free $R$-modules. The complex $C$ is $R_{(0,0)}$-finitely dominated, or of type FP over $R_{(0,0)}$, if it is chain homotopy equivalent to a bounded complex of finitely generated projective $R_{(0,0)}$-modules. We show that this happens if and only if $C$ becomes acyclic after taking tensor product with a certain eight rings of formal power series, the graded analogues of classical Novikov rings. This extends results of Ranicki, Quinn and the first author on Laurent polynomial rings i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.14629","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.14629/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2207.14629","created_at":"2026-05-21T02:04:44.729667+00:00"},{"alias_kind":"arxiv_version","alias_value":"2207.14629v1","created_at":"2026-05-21T02:04:44.729667+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.14629","created_at":"2026-05-21T02:04:44.729667+00:00"},{"alias_kind":"pith_short_12","alias_value":"CMKUOGZ5FCFC","created_at":"2026-05-21T02:04:44.729667+00:00"},{"alias_kind":"pith_short_16","alias_value":"CMKUOGZ5FCFCP3AA","created_at":"2026-05-21T02:04:44.729667+00:00"},{"alias_kind":"pith_short_8","alias_value":"CMKUOGZ5","created_at":"2026-05-21T02:04:44.729667+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/CMKUOGZ5FCFCP3AA3HKUJ3UXBR","json":"https://pith.science/pith/CMKUOGZ5FCFCP3AA3HKUJ3UXBR.json","graph_json":"https://pith.science/api/pith-number/CMKUOGZ5FCFCP3AA3HKUJ3UXBR/graph.json","events_json":"https://pith.science/api/pith-number/CMKUOGZ5FCFCP3AA3HKUJ3UXBR/events.json","paper":"https://pith.science/paper/CMKUOGZ5"},"agent_actions":{"view_html":"https://pith.science/pith/CMKUOGZ5FCFCP3AA3HKUJ3UXBR","download_json":"https://pith.science/pith/CMKUOGZ5FCFCP3AA3HKUJ3UXBR.json","view_paper":"https://pith.science/paper/CMKUOGZ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2207.14629&json=true","fetch_graph":"https://pith.science/api/pith-number/CMKUOGZ5FCFCP3AA3HKUJ3UXBR/graph.json","fetch_events":"https://pith.science/api/pith-number/CMKUOGZ5FCFCP3AA3HKUJ3UXBR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CMKUOGZ5FCFCP3AA3HKUJ3UXBR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CMKUOGZ5FCFCP3AA3HKUJ3UXBR/action/storage_attestation","attest_author":"https://pith.science/pith/CMKUOGZ5FCFCP3AA3HKUJ3UXBR/action/author_attestation","sign_citation":"https://pith.science/pith/CMKUOGZ5FCFCP3AA3HKUJ3UXBR/action/citation_signature","submit_replication":"https://pith.science/pith/CMKUOGZ5FCFCP3AA3HKUJ3UXBR/action/replication_record"}},"created_at":"2026-05-21T02:04:44.729667+00:00","updated_at":"2026-05-21T02:04:44.729667+00:00"}