{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:3GCCJC7ENUA3HYNMRL2LL3HEBC","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":"e56fd694ce6e1ab07bf1b415397b679fec0511497855e0f2e09bb66332dd670f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-03-21T22:03:30Z","title_canon_sha256":"6482048824705929ee9c27134f7a76b7b4d6a25fc58ec5edcb23d2b13d62f47f"},"schema_version":"1.0","source":{"id":"0903.3693","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3693","created_at":"2026-05-18T01:34:55Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3693v3","created_at":"2026-05-18T01:34:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3693","created_at":"2026-05-18T01:34:55Z"},{"alias_kind":"pith_short_12","alias_value":"3GCCJC7ENUA3","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"3GCCJC7ENUA3HYNM","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"3GCCJC7E","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:914dd623d4b81e61196d522be00c44314dd05afbf2ca643eac7ce40d57f326d4","target":"graph","created_at":"2026-05-18T01:34:55Z","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 relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension, via its (birational) cycle map, going to the relative symmetric product. We show the cycle map is the blowing up of the discriminant locus, which consists of cycles with multiple points. We determine the relevant cotangent sheaves and complexes. We determine the structure of certain projective bundles called node scrolls, which play an important role in the geometry of Hilbert schemes.","authors_text":"Ziv Ran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-03-21T22:03:30Z","title":"Structure of the cycle map for Hilbert schemes of families of nodal curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3693","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":"sha256:47f7ff029540a257f72315b002df3f11fedf1c7eac7a1008805146271239ee2c","target":"record","created_at":"2026-05-18T01:34:55Z","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":"e56fd694ce6e1ab07bf1b415397b679fec0511497855e0f2e09bb66332dd670f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-03-21T22:03:30Z","title_canon_sha256":"6482048824705929ee9c27134f7a76b7b4d6a25fc58ec5edcb23d2b13d62f47f"},"schema_version":"1.0","source":{"id":"0903.3693","kind":"arxiv","version":3}},"canonical_sha256":"d984248be46d01b3e1ac8af4b5ece408b06ed838f8f0af712cb0bda9eaccaa6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d984248be46d01b3e1ac8af4b5ece408b06ed838f8f0af712cb0bda9eaccaa6a","first_computed_at":"2026-05-18T01:34:55.895614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:55.895614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TKFnszgKLtglqVE/Er4m68UUGuGxwKlvuwrtUPfCb0zuVZzyrTRJ4/yPnZqaPE3ybUqQzS7aJGswRfk3AMn/Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:55.896373Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.3693","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47f7ff029540a257f72315b002df3f11fedf1c7eac7a1008805146271239ee2c","sha256:914dd623d4b81e61196d522be00c44314dd05afbf2ca643eac7ce40d57f326d4"],"state_sha256":"87c231d46b4a3c4f7f518b3fcf16a7bf06bd2d2c505c3482da05948793d8c77c"}