{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FMKQY6KKUGXEM3KOSDKNHJVZN2","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":"550c7b6138c9570f95d441a6f128b688c8eb8822aed8c9629d38473c6b387016","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-30T13:17:31Z","title_canon_sha256":"039d81e20e74368a80020e4b68a5061812a5f4fa60ceead3daae1ab006209aed"},"schema_version":"1.0","source":{"id":"1605.09217","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09217","created_at":"2026-05-18T00:13:53Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09217v2","created_at":"2026-05-18T00:13:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09217","created_at":"2026-05-18T00:13:53Z"},{"alias_kind":"pith_short_12","alias_value":"FMKQY6KKUGXE","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FMKQY6KKUGXEM3KO","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FMKQY6KK","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:5500a69409250d8293f74b180cba22e840ac5fb511ee0f7f1bc8f992a88d894d","target":"graph","created_at":"2026-05-18T00:13:53Z","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":"For a Cohen-Macaulay ideal of holomorphic functions, we construct by elementary means residue currents whose annihilator is precisely the given ideal. We give two proofs that the currents have the prescribed annihilator, one using the theory of linkage, and another using an explicit division formula involving these residue currents to express the ideal membership.","authors_text":"Emmanuel Mazzilli, Richard L\\\"ark\\\"ang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-30T13:17:31Z","title":"Elementary construction of residue currents associated to Cohen-Macaulay ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09217","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":"sha256:8fd7b26243fed57a949a60540965bc3f25df85b5ff99ed91300e55da2caacb05","target":"record","created_at":"2026-05-18T00:13:53Z","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":"550c7b6138c9570f95d441a6f128b688c8eb8822aed8c9629d38473c6b387016","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-30T13:17:31Z","title_canon_sha256":"039d81e20e74368a80020e4b68a5061812a5f4fa60ceead3daae1ab006209aed"},"schema_version":"1.0","source":{"id":"1605.09217","kind":"arxiv","version":2}},"canonical_sha256":"2b150c794aa1ae466d4e90d4d3a6b96ea74caffd4f532b100973e85ea590c074","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b150c794aa1ae466d4e90d4d3a6b96ea74caffd4f532b100973e85ea590c074","first_computed_at":"2026-05-18T00:13:53.682016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:53.682016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+WGhs9PHMlIokcmtMS/ZCJwCKGPQS/AyB2k83b+DaIbzrM0QU3HAEAhapLR7OxNz0BjCn9n3stEfWPCPBNXNCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:53.682787Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.09217","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fd7b26243fed57a949a60540965bc3f25df85b5ff99ed91300e55da2caacb05","sha256:5500a69409250d8293f74b180cba22e840ac5fb511ee0f7f1bc8f992a88d894d"],"state_sha256":"498de86cbd1311796688c0958939c6721f0a0e2582d7add57d304bb10ffefde3"}