{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PSGCWU7IW6UH5X3WAUASET4HF4","short_pith_number":"pith:PSGCWU7I","canonical_record":{"source":{"id":"1108.2995","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-08-15T13:50:55Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"78d8d6d14aa59e87b8445093bea57f05afc3c078bf58fb0cc8a8eee346eaebf6","abstract_canon_sha256":"9d28d03c2351e7b61b5a100d8e73138e0d7a0747f0a95195a35b5f9f23bf853c"},"schema_version":"1.0"},"canonical_sha256":"7c8c2b53e8b7a87edf760501224f872f0e4e1b359739b0a0519a123047987037","source":{"kind":"arxiv","id":"1108.2995","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2995","created_at":"2026-05-18T03:40:16Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2995v4","created_at":"2026-05-18T03:40:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2995","created_at":"2026-05-18T03:40:16Z"},{"alias_kind":"pith_short_12","alias_value":"PSGCWU7IW6UH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PSGCWU7IW6UH5X3W","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PSGCWU7I","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PSGCWU7IW6UH5X3WAUASET4HF4","target":"record","payload":{"canonical_record":{"source":{"id":"1108.2995","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-08-15T13:50:55Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"78d8d6d14aa59e87b8445093bea57f05afc3c078bf58fb0cc8a8eee346eaebf6","abstract_canon_sha256":"9d28d03c2351e7b61b5a100d8e73138e0d7a0747f0a95195a35b5f9f23bf853c"},"schema_version":"1.0"},"canonical_sha256":"7c8c2b53e8b7a87edf760501224f872f0e4e1b359739b0a0519a123047987037","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:16.416348Z","signature_b64":"XhmKTVO7IUMjZ6eXl/e+kF8jRP75VgIIonyNK/YZDpZhnaZst9pawpd8FH/piL0JX0Ai0sW5H7vftUJ472nTCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c8c2b53e8b7a87edf760501224f872f0e4e1b359739b0a0519a123047987037","last_reissued_at":"2026-05-18T03:40:16.415794Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:16.415794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.2995","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jFV5GH5bOjO/PH+BQp6kdtjPXqe4Y2ndjoDJSglyyGRt0vExfFJdX6gpEpIacfhVU8tsfU4cepafYeorMIUYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:10:33.742290Z"},"content_sha256":"62805a047749ba7e841c35dd7fd01ac5b6e2a1ef965a80d8127f5b002a7d05b2","schema_version":"1.0","event_id":"sha256:62805a047749ba7e841c35dd7fd01ac5b6e2a1ef965a80d8127f5b002a7d05b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PSGCWU7IW6UH5X3WAUASET4HF4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite domination and Novikov rings. Iterative approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.KT","authors_text":"David Quinn, Thomas Huettemann","submitted_at":"2011-08-15T13:50:55Z","abstract_excerpt":"Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,1/x]. Then C is R-finitely dominated, ie, homotopy equivalent over R to a bounded chain complex of finitely generated projective R-modules, if and only if the two chain complexes C((x)) and C((1/x)) are acyclic, as has been proved by Ranicki. Here C((x)) is the tensor product over L of C with the Novikov ring R((x)) = R[[x]][1/x] (also known as the ring of formal Laurent series in x); similarly, C((1/x)) is the tensor product over L of C with the Novikov ring R((1/x)) = R[[1/x]][x]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2995","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/T/ud7TgSa31NJZBctWGHykKIYLKlNgXTNw/1BMhBlw1hAXIVa3xjQ35dW3zt3pDD2ooQ7AKDpdP++Y1WN0uDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:10:33.742662Z"},"content_sha256":"b474f9e2f70e4785b0ef9641b2a8ac544ca728913f8f840e0ce40023b5339698","schema_version":"1.0","event_id":"sha256:b474f9e2f70e4785b0ef9641b2a8ac544ca728913f8f840e0ce40023b5339698"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PSGCWU7IW6UH5X3WAUASET4HF4/bundle.json","state_url":"https://pith.science/pith/PSGCWU7IW6UH5X3WAUASET4HF4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PSGCWU7IW6UH5X3WAUASET4HF4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T00:10:33Z","links":{"resolver":"https://pith.science/pith/PSGCWU7IW6UH5X3WAUASET4HF4","bundle":"https://pith.science/pith/PSGCWU7IW6UH5X3WAUASET4HF4/bundle.json","state":"https://pith.science/pith/PSGCWU7IW6UH5X3WAUASET4HF4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PSGCWU7IW6UH5X3WAUASET4HF4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PSGCWU7IW6UH5X3WAUASET4HF4","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":"9d28d03c2351e7b61b5a100d8e73138e0d7a0747f0a95195a35b5f9f23bf853c","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-08-15T13:50:55Z","title_canon_sha256":"78d8d6d14aa59e87b8445093bea57f05afc3c078bf58fb0cc8a8eee346eaebf6"},"schema_version":"1.0","source":{"id":"1108.2995","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2995","created_at":"2026-05-18T03:40:16Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2995v4","created_at":"2026-05-18T03:40:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2995","created_at":"2026-05-18T03:40:16Z"},{"alias_kind":"pith_short_12","alias_value":"PSGCWU7IW6UH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PSGCWU7IW6UH5X3W","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PSGCWU7I","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:b474f9e2f70e4785b0ef9641b2a8ac544ca728913f8f840e0ce40023b5339698","target":"graph","created_at":"2026-05-18T03:40:16Z","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":"Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,1/x]. Then C is R-finitely dominated, ie, homotopy equivalent over R to a bounded chain complex of finitely generated projective R-modules, if and only if the two chain complexes C((x)) and C((1/x)) are acyclic, as has been proved by Ranicki. Here C((x)) is the tensor product over L of C with the Novikov ring R((x)) = R[[x]][1/x] (also known as the ring of formal Laurent series in x); similarly, C((1/x)) is the tensor product over L of C with the Novikov ring R((1/x)) = R[[1/x]][x].","authors_text":"David Quinn, Thomas Huettemann","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-08-15T13:50:55Z","title":"Finite domination and Novikov rings. Iterative approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2995","kind":"arxiv","version":4},"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":"sha256:62805a047749ba7e841c35dd7fd01ac5b6e2a1ef965a80d8127f5b002a7d05b2","target":"record","created_at":"2026-05-18T03:40:16Z","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":"9d28d03c2351e7b61b5a100d8e73138e0d7a0747f0a95195a35b5f9f23bf853c","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-08-15T13:50:55Z","title_canon_sha256":"78d8d6d14aa59e87b8445093bea57f05afc3c078bf58fb0cc8a8eee346eaebf6"},"schema_version":"1.0","source":{"id":"1108.2995","kind":"arxiv","version":4}},"canonical_sha256":"7c8c2b53e8b7a87edf760501224f872f0e4e1b359739b0a0519a123047987037","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c8c2b53e8b7a87edf760501224f872f0e4e1b359739b0a0519a123047987037","first_computed_at":"2026-05-18T03:40:16.415794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:16.415794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XhmKTVO7IUMjZ6eXl/e+kF8jRP75VgIIonyNK/YZDpZhnaZst9pawpd8FH/piL0JX0Ai0sW5H7vftUJ472nTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:16.416348Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2995","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62805a047749ba7e841c35dd7fd01ac5b6e2a1ef965a80d8127f5b002a7d05b2","sha256:b474f9e2f70e4785b0ef9641b2a8ac544ca728913f8f840e0ce40023b5339698"],"state_sha256":"4cbc868b6ad33b3a7a4557d8995acf1e786a9e23812976bda72dfcc762f10f0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gFbm3v7ELGKSaHIsN+DtvccdurkF+cGV/gLgLGrGGQ4N8vXKFM8+DppnUdy0HX7ZKYmFwll5Cd08uHDRJNgHDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:10:33.744631Z","bundle_sha256":"fae8eb278129116523d745ef72c4c026d9fdcbabbd779997ae460922b97ce54a"}}