{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6KMPH3G3BIILZT42GCEKI3SMGD","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":"89e9ee41e2ef06de4cdab8303d82efba8877551400f69719f04448b558172f4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-04-03T17:54:57Z","title_canon_sha256":"7b64ff5efdd09dd50e19798115c989575ed09cbbf44914fd64980b97970c785c"},"schema_version":"1.0","source":{"id":"1104.0413","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0413","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0413v1","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0413","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"6KMPH3G3BIIL","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6KMPH3G3BIILZT42","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6KMPH3G3","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:c4ea7a8347f714272a9b1f8d6d65fde679f49b67415dceb904899bb1bc050476","target":"graph","created_at":"2026-05-18T04:05:04Z","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 local domain $(R,m)$ of prime characteristic that is a homomorphic image of a Gorenstein ring, Huneke and Lyubeznik proved that there exists a module-finite extension domain $S$ such that the induced map on local cohomology modules $H^i_m(R)\\to H^i_m(S)$ is zero for each $i<\\dim R$. We prove that the extension $S$ may be chosen to be generically Galois, and analyze the Galois groups that arise.","authors_text":"Akiyoshi Sannai, Anurag K. Singh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-04-03T17:54:57Z","title":"Galois extensions, plus closure, and maps on local cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0413","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:acb38d315c35e28e0191a24be01347de28e9325fdf8cbcad5b97857b6bf7b724","target":"record","created_at":"2026-05-18T04:05:04Z","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":"89e9ee41e2ef06de4cdab8303d82efba8877551400f69719f04448b558172f4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-04-03T17:54:57Z","title_canon_sha256":"7b64ff5efdd09dd50e19798115c989575ed09cbbf44914fd64980b97970c785c"},"schema_version":"1.0","source":{"id":"1104.0413","kind":"arxiv","version":1}},"canonical_sha256":"f298f3ecdb0a10bccf9a3088a46e4c30d81739092a82370eeba804923a16b321","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f298f3ecdb0a10bccf9a3088a46e4c30d81739092a82370eeba804923a16b321","first_computed_at":"2026-05-18T04:05:04.005762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:04.005762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UXAYH4KhoNs6VFvImtlnNOxYFvdfJLpVRF7JyKsKQK7AdkxezRWFwoiBle3ubJBbwOL25/P5QDSLGg9J0ahyAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:04.006176Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0413","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acb38d315c35e28e0191a24be01347de28e9325fdf8cbcad5b97857b6bf7b724","sha256:c4ea7a8347f714272a9b1f8d6d65fde679f49b67415dceb904899bb1bc050476"],"state_sha256":"2ad2dd1d42ea2379724497e1603fb8306f67a16e4eccd08a98d4ba4306eabcc8"}