{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GTOYDWWS3SGCW355N2AAZT2P35","short_pith_number":"pith:GTOYDWWS","canonical_record":{"source":{"id":"1809.07118","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-09-19T10:46:24Z","cross_cats_sorted":["math.AT","math.RA"],"title_canon_sha256":"fd42e90b2b84f6fcd280ec0e0666d743b00bec04a627cc8e3b99c81368b23a74","abstract_canon_sha256":"9957d9278aa634bba5f0f5eef71b66b48f3027d00d2e290d2f31f875f91a260a"},"schema_version":"1.0"},"canonical_sha256":"34dd81dad2dc8c2b6fbd6e800ccf4fdf752ad4ae7202511a7140884018720e3b","source":{"kind":"arxiv","id":"1809.07118","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07118","created_at":"2026-05-18T00:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07118v3","created_at":"2026-05-18T00:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07118","created_at":"2026-05-18T00:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"GTOYDWWS3SGC","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GTOYDWWS3SGCW355","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GTOYDWWS","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GTOYDWWS3SGCW355N2AAZT2P35","target":"record","payload":{"canonical_record":{"source":{"id":"1809.07118","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-09-19T10:46:24Z","cross_cats_sorted":["math.AT","math.RA"],"title_canon_sha256":"fd42e90b2b84f6fcd280ec0e0666d743b00bec04a627cc8e3b99c81368b23a74","abstract_canon_sha256":"9957d9278aa634bba5f0f5eef71b66b48f3027d00d2e290d2f31f875f91a260a"},"schema_version":"1.0"},"canonical_sha256":"34dd81dad2dc8c2b6fbd6e800ccf4fdf752ad4ae7202511a7140884018720e3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:21.995215Z","signature_b64":"kbrtaxr3iSfKxlkXyYzUsG2i+VqiGJUvVD4kInhfqlw7QFqUxjhwKcoI6M7uXE4rchFDgWxmeTgmrfshQq5vCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34dd81dad2dc8c2b6fbd6e800ccf4fdf752ad4ae7202511a7140884018720e3b","last_reissued_at":"2026-05-18T00:02:21.994593Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:21.994593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.07118","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3kfL+vCaBX+v6fY4DAzJ36pkYfr805UCovzOJqFsocCx1+cUekzL247sl2nDKFG6fqH0ZeiEVF91fsjcXNiFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:07:44.486060Z"},"content_sha256":"b2b8ed87f1d193c7ae793a7b3e504cd23b5ca1113a589447218a744b708e7b4e","schema_version":"1.0","event_id":"sha256:b2b8ed87f1d193c7ae793a7b3e504cd23b5ca1113a589447218a744b708e7b4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GTOYDWWS3SGCW355N2AAZT2P35","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-commutative localisation and finite domination over strongly Z-graded rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.RA"],"primary_cat":"math.KT","authors_text":"Thomas Huettemann","submitted_at":"2018-09-19T10:46:24Z","abstract_excerpt":"Let R be a strongly Z-graded ring with degree-0 subring S, and let C be a chain complex of modules over the subring P of elements of non-negative degree. We show that there are non-commutative localisations of P which detect whether the complex C is S-finitely dominated or S-contractible, respectively, and that these localisations are universal among P-rings making S-finitely dominated and S-contractible complexes contractible. This generalises known results for polynomial rings to a much wider class of rings. We show by example that in general C need not be P-homotopy finite even if C is S-fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07118","kind":"arxiv","version":3},"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":"2026-05-18T00:02:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3tANRdkIZw53uwCRDIyfLPqiTX7BNdBlHHX/dzQiN12LgOXO9nA0LELtqCi5qfU7uCmAeDonZdlCaD8nQ4e2Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:07:44.486893Z"},"content_sha256":"e7c44fd2a884905500c8f8cea0a3ae9fe96e477b456975b4ffb5813dd1590020","schema_version":"1.0","event_id":"sha256:e7c44fd2a884905500c8f8cea0a3ae9fe96e477b456975b4ffb5813dd1590020"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GTOYDWWS3SGCW355N2AAZT2P35/bundle.json","state_url":"https://pith.science/pith/GTOYDWWS3SGCW355N2AAZT2P35/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GTOYDWWS3SGCW355N2AAZT2P35/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":"2026-06-10T21:07:44Z","links":{"resolver":"https://pith.science/pith/GTOYDWWS3SGCW355N2AAZT2P35","bundle":"https://pith.science/pith/GTOYDWWS3SGCW355N2AAZT2P35/bundle.json","state":"https://pith.science/pith/GTOYDWWS3SGCW355N2AAZT2P35/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GTOYDWWS3SGCW355N2AAZT2P35/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GTOYDWWS3SGCW355N2AAZT2P35","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":"9957d9278aa634bba5f0f5eef71b66b48f3027d00d2e290d2f31f875f91a260a","cross_cats_sorted":["math.AT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-09-19T10:46:24Z","title_canon_sha256":"fd42e90b2b84f6fcd280ec0e0666d743b00bec04a627cc8e3b99c81368b23a74"},"schema_version":"1.0","source":{"id":"1809.07118","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07118","created_at":"2026-05-18T00:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07118v3","created_at":"2026-05-18T00:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07118","created_at":"2026-05-18T00:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"GTOYDWWS3SGC","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GTOYDWWS3SGCW355","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GTOYDWWS","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:e7c44fd2a884905500c8f8cea0a3ae9fe96e477b456975b4ffb5813dd1590020","target":"graph","created_at":"2026-05-18T00:02:21Z","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":"Let R be a strongly Z-graded ring with degree-0 subring S, and let C be a chain complex of modules over the subring P of elements of non-negative degree. We show that there are non-commutative localisations of P which detect whether the complex C is S-finitely dominated or S-contractible, respectively, and that these localisations are universal among P-rings making S-finitely dominated and S-contractible complexes contractible. This generalises known results for polynomial rings to a much wider class of rings. We show by example that in general C need not be P-homotopy finite even if C is S-fi","authors_text":"Thomas Huettemann","cross_cats":["math.AT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-09-19T10:46:24Z","title":"Non-commutative localisation and finite domination over strongly Z-graded rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07118","kind":"arxiv","version":3},"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:b2b8ed87f1d193c7ae793a7b3e504cd23b5ca1113a589447218a744b708e7b4e","target":"record","created_at":"2026-05-18T00:02:21Z","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":"9957d9278aa634bba5f0f5eef71b66b48f3027d00d2e290d2f31f875f91a260a","cross_cats_sorted":["math.AT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-09-19T10:46:24Z","title_canon_sha256":"fd42e90b2b84f6fcd280ec0e0666d743b00bec04a627cc8e3b99c81368b23a74"},"schema_version":"1.0","source":{"id":"1809.07118","kind":"arxiv","version":3}},"canonical_sha256":"34dd81dad2dc8c2b6fbd6e800ccf4fdf752ad4ae7202511a7140884018720e3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34dd81dad2dc8c2b6fbd6e800ccf4fdf752ad4ae7202511a7140884018720e3b","first_computed_at":"2026-05-18T00:02:21.994593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:21.994593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kbrtaxr3iSfKxlkXyYzUsG2i+VqiGJUvVD4kInhfqlw7QFqUxjhwKcoI6M7uXE4rchFDgWxmeTgmrfshQq5vCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:21.995215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.07118","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2b8ed87f1d193c7ae793a7b3e504cd23b5ca1113a589447218a744b708e7b4e","sha256:e7c44fd2a884905500c8f8cea0a3ae9fe96e477b456975b4ffb5813dd1590020"],"state_sha256":"a9db0de2cb2965cb312ec45d1cd841f4d46c4f838e52854b1efaba3e1489d59c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vohMgi0DRNThMFudadLdwBRffac32j+o8xBk7RO/w05z+XAr3BJbkpKjxopqE2A0l0hKDWgtIXVMxpv+nE9fAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:07:44.491833Z","bundle_sha256":"bae4ca840d2d1cc07ce74e8276a801f09f18a21e070d3c2eee7b6056972fddad"}}