{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OVUKEOZINH56GDBISLDNNS3LUU","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":"b190db3037a05f8ea6ab62e8d98e47728e9e21baacebdeaa96d8441c651b81e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-01T02:44:40Z","title_canon_sha256":"78fdd7446eea85c1edcf3711bc635437b327e0e76278fc76a835872dcb31dbb4"},"schema_version":"1.0","source":{"id":"1404.0111","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0111","created_at":"2026-05-18T02:55:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0111v1","created_at":"2026-05-18T02:55:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0111","created_at":"2026-05-18T02:55:05Z"},{"alias_kind":"pith_short_12","alias_value":"OVUKEOZINH56","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OVUKEOZINH56GDBI","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OVUKEOZI","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:6d58fb75053714fe9b5cedf90b3b42dc930fa1fd0f0ecfadb679ec8758deead0","target":"graph","created_at":"2026-05-18T02:55:05Z","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 $(R,\\m)$ be a Noetherian local ring and $M$ a finitely generated $R$-module. Following I. G. Macdonald \\cite{Mac}, the set of all attached primes of the Artinian local cohomology module $H^i_{\\m}(M)$ is denoted by $\\Att_R(H^i_{\\m}(M))$. In \\cite[Theorem 3.7]{Sh}, R. Y. Sharp proved that if $R$ is a quotient of a Gorenstein local ring then the shifted localization principle always holds true, i.e. $$ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\Att_{R_{\\p}}\\big(H^{i-\\dim (R/\\p)}_{\\p R_{\\p}}(M_{\\p})\\big)=\\big\\{\\q R_{\\p}\\mid \\q\\in\\Att_RH^i_{\\m}(M), \\q\\subseteq \\p\\big\\} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\","authors_text":"Le Thanh Nhan, Pham Hung Quy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-01T02:44:40Z","title":"Attached primes of local cohomology modules under localization and completion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0111","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:f169637b37e6d2b1013f73841ad556afb633e5ffc88c1a11d02fbf700a9945cc","target":"record","created_at":"2026-05-18T02:55:05Z","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":"b190db3037a05f8ea6ab62e8d98e47728e9e21baacebdeaa96d8441c651b81e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-01T02:44:40Z","title_canon_sha256":"78fdd7446eea85c1edcf3711bc635437b327e0e76278fc76a835872dcb31dbb4"},"schema_version":"1.0","source":{"id":"1404.0111","kind":"arxiv","version":1}},"canonical_sha256":"7568a23b2869fbe30c2892c6d6cb6ba5138e7860e4fb84b0db67eaf83f64ec07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7568a23b2869fbe30c2892c6d6cb6ba5138e7860e4fb84b0db67eaf83f64ec07","first_computed_at":"2026-05-18T02:55:05.106574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:05.106574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xqdik4fhudT/fPwG4Bo8UvtDLHIy3ziPj1vcIVw74TqAc7zMBqfGEecERaimRPu6JSq2P5ANokv/jMpHx7P6Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:05.107172Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0111","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f169637b37e6d2b1013f73841ad556afb633e5ffc88c1a11d02fbf700a9945cc","sha256:6d58fb75053714fe9b5cedf90b3b42dc930fa1fd0f0ecfadb679ec8758deead0"],"state_sha256":"8de833a4c7f761bfac42b6b5ebab05bbbfa370629cbab1683e4022d6a7a56ab0"}