{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OLFWR6Y76GO5K46TG5TO6JVTJH","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":"f4f76f3c065598330bafd220485be84d36b2df5b61e186f65259d431a71d89e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-11-22T17:10:48Z","title_canon_sha256":"1a88bd074d2d1d9ac5102457ba1df322bda1a87202ac8b289fa5b2bebac1d922"},"schema_version":"1.0","source":{"id":"1611.07423","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07423","created_at":"2026-05-17T23:40:04Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07423v2","created_at":"2026-05-17T23:40:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07423","created_at":"2026-05-17T23:40:04Z"},{"alias_kind":"pith_short_12","alias_value":"OLFWR6Y76GO5","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OLFWR6Y76GO5K46T","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OLFWR6Y7","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:e9c3f7bb7f4e69b3072c98022aec4b99dede9fdaa2d044523696be05c9bfd920","target":"graph","created_at":"2026-05-17T23:40:04Z","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":"In this paper, we study the Severi variety $V_{L,g}$ of genus $g$ curves in $|L|$ on a general polarized K3 surface $(X,L)$. We show that the closure of every component of $V_{L,g}$ contains a component of $V_{L,g-1}$. As a consequence, we see that the general members of every component of $V_{L,g}$ are nodal.","authors_text":"Xi Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-11-22T17:10:48Z","title":"Nodal Curves on K3 Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07423","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":"sha256:24aec95c123af214b097afda99331a9097340369ab60e144dac32ae1b1529555","target":"record","created_at":"2026-05-17T23:40:04Z","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":"f4f76f3c065598330bafd220485be84d36b2df5b61e186f65259d431a71d89e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-11-22T17:10:48Z","title_canon_sha256":"1a88bd074d2d1d9ac5102457ba1df322bda1a87202ac8b289fa5b2bebac1d922"},"schema_version":"1.0","source":{"id":"1611.07423","kind":"arxiv","version":2}},"canonical_sha256":"72cb68fb1ff19dd573d33766ef26b349dda9a5630264ec78f858572e26ddd4fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72cb68fb1ff19dd573d33766ef26b349dda9a5630264ec78f858572e26ddd4fc","first_computed_at":"2026-05-17T23:40:04.971874Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:04.971874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u8kmcDUVDQH4K/aO1Hl00P104eWUwesU8rtInA+vXm3IlKy6Nc8yV9hJF7mglEbE+zJsNU9N3+po4ha6AgPaCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:04.972396Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.07423","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24aec95c123af214b097afda99331a9097340369ab60e144dac32ae1b1529555","sha256:e9c3f7bb7f4e69b3072c98022aec4b99dede9fdaa2d044523696be05c9bfd920"],"state_sha256":"768db7a741167f9283a01f8a0b610742dc32aade0f883c898fa0f2fb7e91762e"}