{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PL2YSTNX47DSKKELPKYQM44UPR","short_pith_number":"pith:PL2YSTNX","canonical_record":{"source":{"id":"1205.4648","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-21T16:18:13Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"8bddcf2da3cc10595f7a380dc4db825861709bf049b6656c1fb79fa52110b712","abstract_canon_sha256":"da3e4888becb2059e4c57cbdd273ce7b8686f7d27d4022c4729563219d847d87"},"schema_version":"1.0"},"canonical_sha256":"7af5894db7e7c725288b7ab10673947c5670e9d4cbf43713e1433bbd159214a2","source":{"kind":"arxiv","id":"1205.4648","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4648","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4648v2","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4648","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"PL2YSTNX47DS","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PL2YSTNX47DSKKEL","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PL2YSTNX","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PL2YSTNX47DSKKELPKYQM44UPR","target":"record","payload":{"canonical_record":{"source":{"id":"1205.4648","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-21T16:18:13Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"8bddcf2da3cc10595f7a380dc4db825861709bf049b6656c1fb79fa52110b712","abstract_canon_sha256":"da3e4888becb2059e4c57cbdd273ce7b8686f7d27d4022c4729563219d847d87"},"schema_version":"1.0"},"canonical_sha256":"7af5894db7e7c725288b7ab10673947c5670e9d4cbf43713e1433bbd159214a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:55.796970Z","signature_b64":"arToMDwvvsa33gAWaRfmcq/fGxhY+GQHF8eySsKjAmL2L6t/apJnZskcjisQY9Nz7a9Oj0IBKfuUutBsrFCVBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7af5894db7e7c725288b7ab10673947c5670e9d4cbf43713e1433bbd159214a2","last_reissued_at":"2026-05-18T01:30:55.796455Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:55.796455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.4648","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":"2026-05-18T01:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6sxfEJ75+YdAGRfi0kpcnqJvjf3nEDfQaG+9ZPMHs6rLqW94km95fL9PUmsV4FVXudYEEk3sjAU0oYkLPS2GDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:26:02.854928Z"},"content_sha256":"1e6c7dd4ead3bcd613ebdb08a85583b2fc867dda4ed992337790f4bccd27893b","schema_version":"1.0","event_id":"sha256:1e6c7dd4ead3bcd613ebdb08a85583b2fc867dda4ed992337790f4bccd27893b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PL2YSTNX47DSKKELPKYQM44UPR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing residue currents of monomial ideals using comparison formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CV","authors_text":"Elizabeth Wulcan, Richard L\\\"ark\\\"ang","submitted_at":"2012-05-21T16:18:13Z","abstract_excerpt":"Given a free resolution of an ideal $\\mathfrak{a}$ of holomorphic functions, one can construct a vector-valued residue current, $R$, which coincides with the classical Coleff-Herrera product if $\\mathfrak{a}$ is a complete intersection ideal and whose annihilator ideal is precisely ~$\\mathfrak{a}$.\n  We give a complete description of $R$ in the case when $\\mathfrak{a}$ is an Artinian monomial ideal and the resolution is the hull resolution (or a more general cellular resolution), extending previous results by the second author. The main ingredient in the proof is a comparison formula for resid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4648","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":"2026-05-18T01:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8/rkV4hpAIvNyP69jgfD0qGDNaO72z3j3fsHl3f0ZwVi0+RjBlvmECHO2vg2gzlHgGZZIE7ZYtarmn87E3qFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:26:02.855275Z"},"content_sha256":"850202284d354519291e06c79a729a5e7a803c184b8f584b88a8f464b07214b0","schema_version":"1.0","event_id":"sha256:850202284d354519291e06c79a729a5e7a803c184b8f584b88a8f464b07214b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PL2YSTNX47DSKKELPKYQM44UPR/bundle.json","state_url":"https://pith.science/pith/PL2YSTNX47DSKKELPKYQM44UPR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PL2YSTNX47DSKKELPKYQM44UPR/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":"2026-06-25T19:26:02Z","links":{"resolver":"https://pith.science/pith/PL2YSTNX47DSKKELPKYQM44UPR","bundle":"https://pith.science/pith/PL2YSTNX47DSKKELPKYQM44UPR/bundle.json","state":"https://pith.science/pith/PL2YSTNX47DSKKELPKYQM44UPR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PL2YSTNX47DSKKELPKYQM44UPR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PL2YSTNX47DSKKELPKYQM44UPR","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":"da3e4888becb2059e4c57cbdd273ce7b8686f7d27d4022c4729563219d847d87","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-21T16:18:13Z","title_canon_sha256":"8bddcf2da3cc10595f7a380dc4db825861709bf049b6656c1fb79fa52110b712"},"schema_version":"1.0","source":{"id":"1205.4648","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4648","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4648v2","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4648","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"PL2YSTNX47DS","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PL2YSTNX47DSKKEL","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PL2YSTNX","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:850202284d354519291e06c79a729a5e7a803c184b8f584b88a8f464b07214b0","target":"graph","created_at":"2026-05-18T01:30:55Z","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 free resolution of an ideal $\\mathfrak{a}$ of holomorphic functions, one can construct a vector-valued residue current, $R$, which coincides with the classical Coleff-Herrera product if $\\mathfrak{a}$ is a complete intersection ideal and whose annihilator ideal is precisely ~$\\mathfrak{a}$.\n  We give a complete description of $R$ in the case when $\\mathfrak{a}$ is an Artinian monomial ideal and the resolution is the hull resolution (or a more general cellular resolution), extending previous results by the second author. The main ingredient in the proof is a comparison formula for resid","authors_text":"Elizabeth Wulcan, Richard L\\\"ark\\\"ang","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-21T16:18:13Z","title":"Computing residue currents of monomial ideals using comparison formulas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4648","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":"sha256:1e6c7dd4ead3bcd613ebdb08a85583b2fc867dda4ed992337790f4bccd27893b","target":"record","created_at":"2026-05-18T01:30:55Z","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":"da3e4888becb2059e4c57cbdd273ce7b8686f7d27d4022c4729563219d847d87","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-21T16:18:13Z","title_canon_sha256":"8bddcf2da3cc10595f7a380dc4db825861709bf049b6656c1fb79fa52110b712"},"schema_version":"1.0","source":{"id":"1205.4648","kind":"arxiv","version":2}},"canonical_sha256":"7af5894db7e7c725288b7ab10673947c5670e9d4cbf43713e1433bbd159214a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7af5894db7e7c725288b7ab10673947c5670e9d4cbf43713e1433bbd159214a2","first_computed_at":"2026-05-18T01:30:55.796455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:55.796455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"arToMDwvvsa33gAWaRfmcq/fGxhY+GQHF8eySsKjAmL2L6t/apJnZskcjisQY9Nz7a9Oj0IBKfuUutBsrFCVBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:55.796970Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4648","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e6c7dd4ead3bcd613ebdb08a85583b2fc867dda4ed992337790f4bccd27893b","sha256:850202284d354519291e06c79a729a5e7a803c184b8f584b88a8f464b07214b0"],"state_sha256":"e8efd3244e9ff20fe478f42eb24868b70e27bcf4281ec54c145eb68dcdc70bb5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LPy0RP4VolAZLkB03cYm0BtbgtgJznD0/tUuqAEsFQ4H/PmXcVEiPEXb/Th3m0j24bjxWiXtUQXH63i+f2jaBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T19:26:02.857203Z","bundle_sha256":"96e63abc7d578d48d2db35b37288587219a93f7b19e8a65b64fa6b0396e63100"}}