{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZS643MMLYBQEJKWPUMM5ZHXUFM","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":"c769b61bd9e466340be35b6d271ae80931073f0b3c49fffad11ab2eb0e4204ad","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AC","submitted_at":"2013-01-06T15:49:13Z","title_canon_sha256":"280d328b56b6381347c3cc956110f794e06ed6e520ac8ff3910706909f62cefa"},"schema_version":"1.0","source":{"id":"1301.1015","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1015","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1015v2","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1015","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZS643MMLYBQE","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZS643MMLYBQEJKWP","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZS643MML","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:a2895b49778bf81ad73068a512cbdedbbbf64f87c33ca7c5d268b44badfa4ee7","target":"graph","created_at":"2026-05-18T02:47:23Z","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":"Some affirmative answers are given to Huneke's problems. The calculation of local cohomology modules with respect to an arbitrary pair of ideals $I,J$ can be reduced to calculation of local cohomology modules with respect to a pair of ideala whose first ideal is generated by any $k$-regular sequence in $I$.","authors_text":"KH. Ahmadi-amoli, M. Aghapournahr, M. Y. Sadeghi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AC","submitted_at":"2013-01-06T15:49:13Z","title":"Some results on the local cohomology modules with respect to a pair of ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1015","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":"sha256:7d3defec50f98b1e10be42feebfeb9eb48d4a6a3fe7ac6db1f40c45c31c74e94","target":"record","created_at":"2026-05-18T02:47:23Z","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":"c769b61bd9e466340be35b6d271ae80931073f0b3c49fffad11ab2eb0e4204ad","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AC","submitted_at":"2013-01-06T15:49:13Z","title_canon_sha256":"280d328b56b6381347c3cc956110f794e06ed6e520ac8ff3910706909f62cefa"},"schema_version":"1.0","source":{"id":"1301.1015","kind":"arxiv","version":2}},"canonical_sha256":"ccbdcdb18bc06044aacfa319dc9ef42b3b705fe939fa095c95dd4db9dc3a80b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccbdcdb18bc06044aacfa319dc9ef42b3b705fe939fa095c95dd4db9dc3a80b3","first_computed_at":"2026-05-18T02:47:23.269755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:23.269755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z8qDPdFQlcbtOhSuBeb0lpNRYoJnEjw3A5eEIeOI7toMVCshmaSAMF28Xp5X6FN0oQf82QmFEPrcpZExjyzzBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:23.270143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1015","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d3defec50f98b1e10be42feebfeb9eb48d4a6a3fe7ac6db1f40c45c31c74e94","sha256:a2895b49778bf81ad73068a512cbdedbbbf64f87c33ca7c5d268b44badfa4ee7"],"state_sha256":"d4c25475e98f967231c9b3ed89402072771756155a1f7ed59017943aafa696dd"}