{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:JTE64K2WPO7RRDZTSO5ZQ2CGVG","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":"f46605674acc359beddb6e19f8ba2a64b31172bf50dcf4d46c75b70bbe85a22c","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-06-18T18:12:54Z","title_canon_sha256":"3445b8d74c578afb4fb93eae13dfff3ad523ba2e62851cbc649990f68c734c1c"},"schema_version":"1.0","source":{"id":"0806.3056","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.3056","created_at":"2026-05-18T04:04:04Z"},{"alias_kind":"arxiv_version","alias_value":"0806.3056v3","created_at":"2026-05-18T04:04:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.3056","created_at":"2026-05-18T04:04:04Z"},{"alias_kind":"pith_short_12","alias_value":"JTE64K2WPO7R","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"JTE64K2WPO7RRDZT","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"JTE64K2W","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:2a61350fb34dff56147ab4d9d8718bcad0931e3743d8e2cfeb0c70936eb1b4ec","target":"graph","created_at":"2026-05-18T04:04:04Z","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":"We show that the secant variety of a linearly normal smooth curve of degree at least 2g+3 is arithmetically Cohen-Macaulay, and we use this information to study the graded Betti numbers of the secant variety.","authors_text":"Jessica Sidman, Peter Vermeire","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-06-18T18:12:54Z","title":"Syzygies of the secant variety of a curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.3056","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":"sha256:15218be27bd8379db22204091dab17fd6bc9cb9eb98339706dbdea08db28a3fd","target":"record","created_at":"2026-05-18T04:04:04Z","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":"f46605674acc359beddb6e19f8ba2a64b31172bf50dcf4d46c75b70bbe85a22c","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-06-18T18:12:54Z","title_canon_sha256":"3445b8d74c578afb4fb93eae13dfff3ad523ba2e62851cbc649990f68c734c1c"},"schema_version":"1.0","source":{"id":"0806.3056","kind":"arxiv","version":3}},"canonical_sha256":"4cc9ee2b567bbf188f3393bb986846a9ab56ec38a36df9390fda618012d594ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cc9ee2b567bbf188f3393bb986846a9ab56ec38a36df9390fda618012d594ee","first_computed_at":"2026-05-18T04:04:04.802618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:04.802618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2XM76TXH2Q2D2OV17SOrCEH5wJn7VvIZL95L4ROgOGrj3MR/tnXRM1z5ZqF2NQ3rcJEP/EL8RjtdNDxbkZUSDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:04.803133Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.3056","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15218be27bd8379db22204091dab17fd6bc9cb9eb98339706dbdea08db28a3fd","sha256:2a61350fb34dff56147ab4d9d8718bcad0931e3743d8e2cfeb0c70936eb1b4ec"],"state_sha256":"e00937c8ef4ca8ba6f73ad68887053d85fa0bdd2234cb9d970e6e6abfec7e72b"}