{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:CMKUOGZ5FCFCP3AA3HKUJ3UXBR","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":"8ac7474aa6d5c0466fc72560ed611009fd380b1f86baa1139a137047909ca95c","cross_cats_sorted":["math.AC","math.AT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2022-07-29T12:12:43Z","title_canon_sha256":"30fb8911596016117f117b9dc32822d338e08efb1e00642b6455599541e2aca7"},"schema_version":"1.0","source":{"id":"2207.14629","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.14629","created_at":"2026-05-21T02:04:44Z"},{"alias_kind":"arxiv_version","alias_value":"2207.14629v1","created_at":"2026-05-21T02:04:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.14629","created_at":"2026-05-21T02:04:44Z"},{"alias_kind":"pith_short_12","alias_value":"CMKUOGZ5FCFC","created_at":"2026-05-21T02:04:44Z"},{"alias_kind":"pith_short_16","alias_value":"CMKUOGZ5FCFCP3AA","created_at":"2026-05-21T02:04:44Z"},{"alias_kind":"pith_short_8","alias_value":"CMKUOGZ5","created_at":"2026-05-21T02:04:44Z"}],"graph_snapshots":[{"event_id":"sha256:04ef1af1f0623ff89842f300fea452576225e86e891f5743a1030f8e9289c2c2","target":"graph","created_at":"2026-05-21T02:04:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2207.14629/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Luke Steers, Thomas Huettemann","cross_cats":["math.AC","math.AT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2022-07-29T12:12:43Z","title":"Finite domination and Novikov homology over strongly $\\mathbb{Z}^2$-graded rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.14629","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:d1541aa66bb57583fac386a9ab476344360626f93d35e51940114048a7c568d3","target":"record","created_at":"2026-05-21T02:04:44Z","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":"8ac7474aa6d5c0466fc72560ed611009fd380b1f86baa1139a137047909ca95c","cross_cats_sorted":["math.AC","math.AT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2022-07-29T12:12:43Z","title_canon_sha256":"30fb8911596016117f117b9dc32822d338e08efb1e00642b6455599541e2aca7"},"schema_version":"1.0","source":{"id":"2207.14629","kind":"arxiv","version":1}},"canonical_sha256":"1315471b3d288a27ec00d9d544ee970c6919da253f25c825b07d64bbbdf13fd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1315471b3d288a27ec00d9d544ee970c6919da253f25c825b07d64bbbdf13fd7","first_computed_at":"2026-05-21T02:04:44.729538Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T02:04:44.729538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yLquue17oGvMdQSWgW/KH8cOVSmOA2ZGR3zboa3cJakuiXdDvPZHzCqWbE+zN+i+u5k3pIk7XOfX4h/OJTfUBw==","signature_status":"signed_v1","signed_at":"2026-05-21T02:04:44.730381Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.14629","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1541aa66bb57583fac386a9ab476344360626f93d35e51940114048a7c568d3","sha256:04ef1af1f0623ff89842f300fea452576225e86e891f5743a1030f8e9289c2c2"],"state_sha256":"8f650461e2dd0c23ce6d47d71b5422f5d68f9f6aa600a613f18e8e8f187458d7"}