{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZTXERTVS6TEI2ZZMT3PKWINCZ2","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":"75d521f1e2093a831dca6328a31edd19e850421b45aa83b2b4443a448c209b27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-10-04T07:14:55Z","title_canon_sha256":"c4e7931bdc1d5c1a0b8f1a8b6a552d8f39873af1ff31849de09244fc02aa1f26"},"schema_version":"1.0","source":{"id":"1810.02077","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02077","created_at":"2026-05-17T23:44:38Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02077v3","created_at":"2026-05-17T23:44:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02077","created_at":"2026-05-17T23:44:38Z"},{"alias_kind":"pith_short_12","alias_value":"ZTXERTVS6TEI","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZTXERTVS6TEI2ZZM","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZTXERTVS","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:dae26963ca7f5e1eb51911517f6b1ab40bd65c354cdb400a6c87d5b36ce8a605","target":"graph","created_at":"2026-05-17T23:44:38Z","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":"We study the defining equations of the Rees algebra of ideals arising from curve parametrizations in the plane and in rational normal scrolls, inspired by the work of Madsen and Kustin, Polini and Ulrich. The curves are related by work of Bernardi, Gimigliano and Ida, and we use this framework to relate the defining equations.","authors_text":"Carlos D'Andrea, David Cox, Teresa Cortadellas Benitez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-10-04T07:14:55Z","title":"The Rees Algebra of Parametric Curves via liftings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02077","kind":"arxiv","version":3},"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":"sha256:3bd584c7cb7804df75092da5e27d588abc9bd178727d280f4426cbf5810251c0","target":"record","created_at":"2026-05-17T23:44:38Z","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":"75d521f1e2093a831dca6328a31edd19e850421b45aa83b2b4443a448c209b27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-10-04T07:14:55Z","title_canon_sha256":"c4e7931bdc1d5c1a0b8f1a8b6a552d8f39873af1ff31849de09244fc02aa1f26"},"schema_version":"1.0","source":{"id":"1810.02077","kind":"arxiv","version":3}},"canonical_sha256":"ccee48ceb2f4c88d672c9edeab21a2ce9678ffac53585450db92258230703b88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccee48ceb2f4c88d672c9edeab21a2ce9678ffac53585450db92258230703b88","first_computed_at":"2026-05-17T23:44:38.021593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:38.021593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i7G8eFhM+yCAZI7aNJrMFWm/BO13pkXJKdhfxZ2oG+eeHW70odNc5PpT3mOUsXwSQPyLYTBjMX7bO0YePb47CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:38.021959Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.02077","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bd584c7cb7804df75092da5e27d588abc9bd178727d280f4426cbf5810251c0","sha256:dae26963ca7f5e1eb51911517f6b1ab40bd65c354cdb400a6c87d5b36ce8a605"],"state_sha256":"c39371d7827ab0e453c4c5de8d09dab0e4e3c66ef05abb561b61b7df4df189c9"}