{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AIJNOLS67AXOWVPVFE23F7W3CO","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":"1d6a7c917e93db9f983763061371317216475e90b875bc6a57afbe7240453d7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-17T05:34:42Z","title_canon_sha256":"1f8db2f6cdcf29512cc2da30c5f1260234ae051de4b0201280fe0076dcf4c456"},"schema_version":"1.0","source":{"id":"1905.07116","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07116","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07116v1","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07116","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"pith_short_12","alias_value":"AIJNOLS67AXO","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AIJNOLS67AXOWVPV","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AIJNOLS6","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:aacd00989e023efc92f0ebd30f3a7bc982677d39fc4795238caffce1ba256176","target":"graph","created_at":"2026-05-17T23:45:57Z","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":"Let $X$ be a smooth projective surface and $L\\in \\mathrm{Pic}(X)$. We prove that if $L$ is $(2k-1)$-spanned, then the set $\\tilde{V}_k(L)$ of all nodal and irreducible $D\\in |L|$ with exactly $k$ nodes is irreducible. The set $\\tilde{V}_k(L)$ is an open subset of a Severi variety of $|L|$, the full Severi variety parametrizing all integral $D\\in |L|$ with geometric genus $g(L)-k$.","authors_text":"Edoardo Ballico","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-17T05:34:42Z","title":"On the irreducibility of the Severi variety of nodal curves in a smooth surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07116","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":"sha256:87b835a78a0ad31567cbce8c70287961f4b0cec7f1650190ab14c1563760cd1c","target":"record","created_at":"2026-05-17T23:45:57Z","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":"1d6a7c917e93db9f983763061371317216475e90b875bc6a57afbe7240453d7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-17T05:34:42Z","title_canon_sha256":"1f8db2f6cdcf29512cc2da30c5f1260234ae051de4b0201280fe0076dcf4c456"},"schema_version":"1.0","source":{"id":"1905.07116","kind":"arxiv","version":1}},"canonical_sha256":"0212d72e5ef82eeb55f52935b2fedb13a97c3754788aff422cbbb71bfe1676df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0212d72e5ef82eeb55f52935b2fedb13a97c3754788aff422cbbb71bfe1676df","first_computed_at":"2026-05-17T23:45:57.266967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:57.266967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AeAknP14B1HdVdqK19/AYPC72scZNyscKmbul9X2nqiaeTUEkF4pyoIgLr8YUPvWcU2efKxrMMcmUicH76iPAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:57.267581Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.07116","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87b835a78a0ad31567cbce8c70287961f4b0cec7f1650190ab14c1563760cd1c","sha256:aacd00989e023efc92f0ebd30f3a7bc982677d39fc4795238caffce1ba256176"],"state_sha256":"ceadd29565d77bcdb47e9108a743cb5d25ff0dbf7ab928cc94c0e733ae1120a4"}