{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:H3ENOTGNUKHVEDQPMUAXX7MQUB","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":"7316a9e4e46871e6e1ae1a734afe1185c2905b85c106776effa9f4a768f044cc","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-11T20:53:59Z","title_canon_sha256":"6581289693297a2521aa5a0f60dff4cced0d235e1ac8a3681ea0d8267db4d25f"},"schema_version":"1.0","source":{"id":"0911.2221","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2221","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2221v3","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2221","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"H3ENOTGNUKHV","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"H3ENOTGNUKHVEDQP","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"H3ENOTGN","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:ba4351c517380141031316db8f3fce565851690740ae26631e6f0e70b7b9d02d","target":"graph","created_at":"2026-05-18T03:40:26Z","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 if $D \\subset \\mathbb P^N$ is obtained from a codimension two local complete intersection $C$ by adding embedded points of multiplicity $\\leq 3$, then $D$ is a flat limit of $C$ and isolated points. As applications, we determine the irreducible components of Hilbert schemes of space curves with high arithmetic genus, show the smoothness of the Hilbert component whose general member is a plane curve union a point in $\\mathbb P^3$, and construct a Hilbert component whose general member has an embedded point.","authors_text":"Dawei Chen, Scott Nollet","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-11T20:53:59Z","title":"Detaching embedded points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2221","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":"sha256:07b0520a09f8a2ee7d023927c406383eb2445387583b88320416ee5265938e99","target":"record","created_at":"2026-05-18T03:40:26Z","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":"7316a9e4e46871e6e1ae1a734afe1185c2905b85c106776effa9f4a768f044cc","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-11T20:53:59Z","title_canon_sha256":"6581289693297a2521aa5a0f60dff4cced0d235e1ac8a3681ea0d8267db4d25f"},"schema_version":"1.0","source":{"id":"0911.2221","kind":"arxiv","version":3}},"canonical_sha256":"3ec8d74ccda28f520e0f65017bfd90a04dbd2fd104f4e0d9da262e97d7f3d003","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ec8d74ccda28f520e0f65017bfd90a04dbd2fd104f4e0d9da262e97d7f3d003","first_computed_at":"2026-05-18T03:40:26.425712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:26.425712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z0Ya/jBF0QsmDy9EMwKzJMAwQIAGvcRZM0iLOtGfiCbG71miVgZT1BVotMslNjKFdgizfPnQ4KGGZMX8vz7FBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:26.426528Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.2221","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07b0520a09f8a2ee7d023927c406383eb2445387583b88320416ee5265938e99","sha256:ba4351c517380141031316db8f3fce565851690740ae26631e6f0e70b7b9d02d"],"state_sha256":"a656823e898970122c8769e1c8248db45e2c8afd8bb84ed2e4c20d36e6e898bd"}