{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CSFUNX2LSWNV5YGQUHFLY2KNJB","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":"9f825b147b38820e84ad4607de3b0f14a17229f2f866d8d05a51133b6053d091","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-12T17:30:52Z","title_canon_sha256":"3a6be5d5b9f4d9cfd4cb87e7daf89ad86f2b6b7262693f411caee2d4d83d3645"},"schema_version":"1.0","source":{"id":"1409.3801","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3801","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3801v1","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3801","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"pith_short_12","alias_value":"CSFUNX2LSWNV","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CSFUNX2LSWNV5YGQ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CSFUNX2L","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:8930ab4609197dc0a94eec04ed83db7abca1ff6918627fe52d3a88659b13ab6a","target":"graph","created_at":"2026-05-18T02:42:54Z","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":"A multiple (loc. Cohen Macaulay) structure, X, on a space curve C in P3 is said to be primitive if X is locally contained in a smooth surface. We give numerical conditions for C to be a \"primitive\" set theoretic complete intersection (i.e. to have a primitive multiple structure which is a complete intersection).","authors_text":"Philippe Ellia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-12T17:30:52Z","title":"Complete intersections primitive structures on space curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3801","kind":"arxiv","version":1},"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:a02472fea317514c8c37144953358e1c737838a5378f8781c86f75333204c455","target":"record","created_at":"2026-05-18T02:42:54Z","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":"9f825b147b38820e84ad4607de3b0f14a17229f2f866d8d05a51133b6053d091","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-12T17:30:52Z","title_canon_sha256":"3a6be5d5b9f4d9cfd4cb87e7daf89ad86f2b6b7262693f411caee2d4d83d3645"},"schema_version":"1.0","source":{"id":"1409.3801","kind":"arxiv","version":1}},"canonical_sha256":"148b46df4b959b5ee0d0a1cabc694d4846dfeca75d705279d9c7a44d18aa57cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"148b46df4b959b5ee0d0a1cabc694d4846dfeca75d705279d9c7a44d18aa57cd","first_computed_at":"2026-05-18T02:42:54.654590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:54.654590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AeYr2EPL3OtQOgorxgfi2M5zS5DoS/U1eQtmDl3YFjJ12zfO4//r6kuW0AsyBU3zWR+WMXjaAOJQEA6NnqmcDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:54.654940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3801","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a02472fea317514c8c37144953358e1c737838a5378f8781c86f75333204c455","sha256:8930ab4609197dc0a94eec04ed83db7abca1ff6918627fe52d3a88659b13ab6a"],"state_sha256":"1956af4aebf251fa715315eab9efbd541ceade54d7dcea9a36d9d9478353091c"}