{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BYDDEC7NTQLGJ4Z4SA4BJJ4F6B","short_pith_number":"pith:BYDDEC7N","canonical_record":{"source":{"id":"1802.06491","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-19T02:02:36Z","cross_cats_sorted":[],"title_canon_sha256":"e064bd4796a0a1b46d1cf41db49be3ca85583d33118675bb37703d8796d07d0d","abstract_canon_sha256":"8268761cd96cf7996321fc52b3e1abb6fc11c9ef6307162650255993657d8208"},"schema_version":"1.0"},"canonical_sha256":"0e06320bed9c1664f33c903814a785f0506fc578e387f86d3207d152a53f8a4f","source":{"kind":"arxiv","id":"1802.06491","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06491","created_at":"2026-05-18T00:19:02Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06491v2","created_at":"2026-05-18T00:19:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06491","created_at":"2026-05-18T00:19:02Z"},{"alias_kind":"pith_short_12","alias_value":"BYDDEC7NTQLG","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BYDDEC7NTQLGJ4Z4","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BYDDEC7N","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BYDDEC7NTQLGJ4Z4SA4BJJ4F6B","target":"record","payload":{"canonical_record":{"source":{"id":"1802.06491","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-19T02:02:36Z","cross_cats_sorted":[],"title_canon_sha256":"e064bd4796a0a1b46d1cf41db49be3ca85583d33118675bb37703d8796d07d0d","abstract_canon_sha256":"8268761cd96cf7996321fc52b3e1abb6fc11c9ef6307162650255993657d8208"},"schema_version":"1.0"},"canonical_sha256":"0e06320bed9c1664f33c903814a785f0506fc578e387f86d3207d152a53f8a4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:02.352350Z","signature_b64":"2tMqowfMApSaM2CQYMhg1cj8jIbz6z7kqgpEtg0m/QgH/1HzDIBHx1LPN8jA5XI086COGRs2vgkm5DwLIZkDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e06320bed9c1664f33c903814a785f0506fc578e387f86d3207d152a53f8a4f","last_reissued_at":"2026-05-18T00:19:02.351559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:02.351559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.06491","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gw4D8AYXtun1eeaWsOVgq/Cwlnq//Jej0e/nsXh5soeryFSF+McT/iso/kTaBZ5eVbCAX5PbEX1xtEQ/9pUzBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:14:48.775275Z"},"content_sha256":"febb8611cd1350092309e41f63413cfcdb73a327e9c77d871310e19cdf2dce44","schema_version":"1.0","event_id":"sha256:febb8611cd1350092309e41f63413cfcdb73a327e9c77d871310e19cdf2dce44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BYDDEC7NTQLGJ4Z4SA4BJJ4F6B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trace Ideals and the Gorenstein Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Haydee Lindo, Nina Pande","submitted_at":"2018-02-19T02:02:36Z","abstract_excerpt":"Let R be a local Noetherian commutative ring. We prove that R is an Artinian Gorenstein ring if and only if every ideal in R is a trace ideal. We discuss when the trace ideal of a module coincides with its double annihilator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06491","kind":"arxiv","version":2},"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":"2026-05-18T00:19:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8d88BUnVmEa+jxjdWSqurCOokkDa/npcSiU0DcH4WcB21AfFWd5kJ8kA24a5wyF8F4oqn93H6asAblnEc6u0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:14:48.775874Z"},"content_sha256":"7d0f7a89e59cad01abd6a512e30e73be80272c03886b5763ad9a680a473cbabb","schema_version":"1.0","event_id":"sha256:7d0f7a89e59cad01abd6a512e30e73be80272c03886b5763ad9a680a473cbabb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BYDDEC7NTQLGJ4Z4SA4BJJ4F6B/bundle.json","state_url":"https://pith.science/pith/BYDDEC7NTQLGJ4Z4SA4BJJ4F6B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BYDDEC7NTQLGJ4Z4SA4BJJ4F6B/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":"2026-06-01T00:14:48Z","links":{"resolver":"https://pith.science/pith/BYDDEC7NTQLGJ4Z4SA4BJJ4F6B","bundle":"https://pith.science/pith/BYDDEC7NTQLGJ4Z4SA4BJJ4F6B/bundle.json","state":"https://pith.science/pith/BYDDEC7NTQLGJ4Z4SA4BJJ4F6B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BYDDEC7NTQLGJ4Z4SA4BJJ4F6B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BYDDEC7NTQLGJ4Z4SA4BJJ4F6B","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":"8268761cd96cf7996321fc52b3e1abb6fc11c9ef6307162650255993657d8208","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-19T02:02:36Z","title_canon_sha256":"e064bd4796a0a1b46d1cf41db49be3ca85583d33118675bb37703d8796d07d0d"},"schema_version":"1.0","source":{"id":"1802.06491","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06491","created_at":"2026-05-18T00:19:02Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06491v2","created_at":"2026-05-18T00:19:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06491","created_at":"2026-05-18T00:19:02Z"},{"alias_kind":"pith_short_12","alias_value":"BYDDEC7NTQLG","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BYDDEC7NTQLGJ4Z4","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BYDDEC7N","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:7d0f7a89e59cad01abd6a512e30e73be80272c03886b5763ad9a680a473cbabb","target":"graph","created_at":"2026-05-18T00:19:02Z","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 local Noetherian commutative ring. We prove that R is an Artinian Gorenstein ring if and only if every ideal in R is a trace ideal. We discuss when the trace ideal of a module coincides with its double annihilator.","authors_text":"Haydee Lindo, Nina Pande","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-19T02:02:36Z","title":"Trace Ideals and the Gorenstein Property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06491","kind":"arxiv","version":2},"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:febb8611cd1350092309e41f63413cfcdb73a327e9c77d871310e19cdf2dce44","target":"record","created_at":"2026-05-18T00:19:02Z","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":"8268761cd96cf7996321fc52b3e1abb6fc11c9ef6307162650255993657d8208","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-19T02:02:36Z","title_canon_sha256":"e064bd4796a0a1b46d1cf41db49be3ca85583d33118675bb37703d8796d07d0d"},"schema_version":"1.0","source":{"id":"1802.06491","kind":"arxiv","version":2}},"canonical_sha256":"0e06320bed9c1664f33c903814a785f0506fc578e387f86d3207d152a53f8a4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e06320bed9c1664f33c903814a785f0506fc578e387f86d3207d152a53f8a4f","first_computed_at":"2026-05-18T00:19:02.351559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:02.351559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2tMqowfMApSaM2CQYMhg1cj8jIbz6z7kqgpEtg0m/QgH/1HzDIBHx1LPN8jA5XI086COGRs2vgkm5DwLIZkDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:02.352350Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.06491","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:febb8611cd1350092309e41f63413cfcdb73a327e9c77d871310e19cdf2dce44","sha256:7d0f7a89e59cad01abd6a512e30e73be80272c03886b5763ad9a680a473cbabb"],"state_sha256":"3e555eeee91b847595a947526323214e00185ca90867e00232c6023201f7b3ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S1TqSNRpKVDkC5cHlJk0Vtt5n6tmBgpS7KuIWxkSf6Ff8AKgdyknIPKmjLX+EhclKUshXAwFIcdBRwjm7UBRCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:14:48.778811Z","bundle_sha256":"d4c00c19f2b1dbca68701fae8fc4955c8612771882f006a8af5e70a59519ecdd"}}