{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:WZW34IOOALJDA3RJKLM6QKAV64","short_pith_number":"pith:WZW34IOO","canonical_record":{"source":{"id":"1212.0131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-12-01T16:42:48Z","cross_cats_sorted":[],"title_canon_sha256":"eb1383796b54b5b31a83c68e2b6769ba249e87c82d89b2641c680f34580a965e","abstract_canon_sha256":"6252d1743d462b817edcf6295cca315b1cb3db6d3450dd9b09fd0325acbfe4f0"},"schema_version":"1.0"},"canonical_sha256":"b66dbe21ce02d2306e2952d9e82815f724945888d6caf81044c5d2e182d04194","source":{"kind":"arxiv","id":"1212.0131","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0131","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0131v1","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0131","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"WZW34IOOALJD","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WZW34IOOALJDA3RJ","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WZW34IOO","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:WZW34IOOALJDA3RJKLM6QKAV64","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-12-01T16:42:48Z","cross_cats_sorted":[],"title_canon_sha256":"eb1383796b54b5b31a83c68e2b6769ba249e87c82d89b2641c680f34580a965e","abstract_canon_sha256":"6252d1743d462b817edcf6295cca315b1cb3db6d3450dd9b09fd0325acbfe4f0"},"schema_version":"1.0"},"canonical_sha256":"b66dbe21ce02d2306e2952d9e82815f724945888d6caf81044c5d2e182d04194","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:27.172494Z","signature_b64":"wX9ssPuWGhO+H2xNcg7cMDI362poDCy6Ennc9d+DTfkcTrp9m3cTjw/mzftBQR4C5JWPjyHRlCTb6AWxYdqeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b66dbe21ce02d2306e2952d9e82815f724945888d6caf81044c5d2e182d04194","last_reissued_at":"2026-05-18T03:39:27.171858Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:27.171858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0131","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k7nzg81Sq7gBjmyB8YO0OSHtgb0kDWw/lT8YzPogdosOEpMfCnZu3oDVfwa+ECCgJJ2sKQsgeihk2s+tZLJDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:00:23.792993Z"},"content_sha256":"f0cfd6fe1440b17a0142990609190b2873a4cdf1b0e2ba66aeb6da79d2790383","schema_version":"1.0","event_id":"sha256:f0cfd6fe1440b17a0142990609190b2873a4cdf1b0e2ba66aeb6da79d2790383"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:WZW34IOOALJDA3RJKLM6QKAV64","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reflexivity and connectedness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Sean Sather-Wagstaff","submitted_at":"2012-12-01T16:42:48Z","abstract_excerpt":"Given a finitely generated module over a commutative noetherian ring that satisfies certain reflexivity conditions, we show how failure of the semidualizing property for the module manifests in a disconnection of the prime spectrum of the ring."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0131","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IJjqmOSn5tHQ/WLOekZ2nE8ae+zwgNKSDQxK1+AHkTv23TsLXBweQVxFBSGnr0sOAr9P7+KTefO2nr+RLuYZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:00:23.793401Z"},"content_sha256":"862ba907271d54abe3d11efffd6699c300dd3e89a846b268bb6b45bae4581d44","schema_version":"1.0","event_id":"sha256:862ba907271d54abe3d11efffd6699c300dd3e89a846b268bb6b45bae4581d44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WZW34IOOALJDA3RJKLM6QKAV64/bundle.json","state_url":"https://pith.science/pith/WZW34IOOALJDA3RJKLM6QKAV64/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WZW34IOOALJDA3RJKLM6QKAV64/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":"2026-06-06T19:00:23Z","links":{"resolver":"https://pith.science/pith/WZW34IOOALJDA3RJKLM6QKAV64","bundle":"https://pith.science/pith/WZW34IOOALJDA3RJKLM6QKAV64/bundle.json","state":"https://pith.science/pith/WZW34IOOALJDA3RJKLM6QKAV64/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WZW34IOOALJDA3RJKLM6QKAV64/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WZW34IOOALJDA3RJKLM6QKAV64","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":"6252d1743d462b817edcf6295cca315b1cb3db6d3450dd9b09fd0325acbfe4f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-12-01T16:42:48Z","title_canon_sha256":"eb1383796b54b5b31a83c68e2b6769ba249e87c82d89b2641c680f34580a965e"},"schema_version":"1.0","source":{"id":"1212.0131","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0131","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0131v1","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0131","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"WZW34IOOALJD","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WZW34IOOALJDA3RJ","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WZW34IOO","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:862ba907271d54abe3d11efffd6699c300dd3e89a846b268bb6b45bae4581d44","target":"graph","created_at":"2026-05-18T03:39:27Z","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":"Given a finitely generated module over a commutative noetherian ring that satisfies certain reflexivity conditions, we show how failure of the semidualizing property for the module manifests in a disconnection of the prime spectrum of the ring.","authors_text":"Sean Sather-Wagstaff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-12-01T16:42:48Z","title":"Reflexivity and connectedness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0131","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:f0cfd6fe1440b17a0142990609190b2873a4cdf1b0e2ba66aeb6da79d2790383","target":"record","created_at":"2026-05-18T03:39:27Z","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":"6252d1743d462b817edcf6295cca315b1cb3db6d3450dd9b09fd0325acbfe4f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-12-01T16:42:48Z","title_canon_sha256":"eb1383796b54b5b31a83c68e2b6769ba249e87c82d89b2641c680f34580a965e"},"schema_version":"1.0","source":{"id":"1212.0131","kind":"arxiv","version":1}},"canonical_sha256":"b66dbe21ce02d2306e2952d9e82815f724945888d6caf81044c5d2e182d04194","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b66dbe21ce02d2306e2952d9e82815f724945888d6caf81044c5d2e182d04194","first_computed_at":"2026-05-18T03:39:27.171858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:27.171858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wX9ssPuWGhO+H2xNcg7cMDI362poDCy6Ennc9d+DTfkcTrp9m3cTjw/mzftBQR4C5JWPjyHRlCTb6AWxYdqeDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:27.172494Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0131","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0cfd6fe1440b17a0142990609190b2873a4cdf1b0e2ba66aeb6da79d2790383","sha256:862ba907271d54abe3d11efffd6699c300dd3e89a846b268bb6b45bae4581d44"],"state_sha256":"583f94e0c5fd7229ab46d8989f0d8d63eecb033c00921c292dc9fe6c9c2ece89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2XznpzvopSZCZDPqOuFd1rX1b8KtMAngVFJW1hTZm+UD6P9O8Gmk+4DNhNX6dZnVOf8ljADqDyRazIVsvNRGCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:00:23.796283Z","bundle_sha256":"585c66bbb661436118e2e7b25b89306eff25d719920401e3007082157762683e"}}