{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3HPCA6LGA2LRDYTPBGYJVCIGOB","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":"98046136a2337c12b3ad2aa5fdea4be5ba51956e512ac0e1485c6faf2e69ecf7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-30T19:51:37Z","title_canon_sha256":"20ea39449c3fcd57530c6282504f38dff66aa2a019fc4a253a6704ff3638f3ac"},"schema_version":"1.0","source":{"id":"1208.6282","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.6282","created_at":"2026-05-18T03:46:46Z"},{"alias_kind":"arxiv_version","alias_value":"1208.6282v1","created_at":"2026-05-18T03:46:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6282","created_at":"2026-05-18T03:46:46Z"},{"alias_kind":"pith_short_12","alias_value":"3HPCA6LGA2LR","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3HPCA6LGA2LRDYTP","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3HPCA6LG","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:542c2ab07772c4a9ee37e1ab65a9011ab5c92f3454cd175a1334ab29ae428bc1","target":"graph","created_at":"2026-05-18T03:46:46Z","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":"Recently Knutsen found criteria for the curves in a complete linear system $|\\mathcal{L}|$ on a smooth surface $X$ in a nodal K-trivial threefold $Y_0$ to deform to a scheme of finitely many smooth isolated curves in a general deformation $Y_t$ of $Y_0$. In this article we develop new methods to check whether the set of nodes of $Y_0$ imposes independent conditions on $|\\mathcal{L}|$. As an application, we find new smooth isolated curves in complete intersection Calabi-Yau threefolds.","authors_text":"Xun Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-30T19:51:37Z","title":"On smooth and isolated curves in general complete intersection Calabi-Yau threefolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6282","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":"sha256:3d66017ab43854d8162aa141ae4a5859c5c391269e8e785fdd51fd4df5e3b9f8","target":"record","created_at":"2026-05-18T03:46:46Z","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":"98046136a2337c12b3ad2aa5fdea4be5ba51956e512ac0e1485c6faf2e69ecf7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-30T19:51:37Z","title_canon_sha256":"20ea39449c3fcd57530c6282504f38dff66aa2a019fc4a253a6704ff3638f3ac"},"schema_version":"1.0","source":{"id":"1208.6282","kind":"arxiv","version":1}},"canonical_sha256":"d9de207966069711e26f09b09a89067060c5a2349410a81b3186cd78d3565dec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9de207966069711e26f09b09a89067060c5a2349410a81b3186cd78d3565dec","first_computed_at":"2026-05-18T03:46:46.007717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:46.007717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lVN3zJ9DR/f1czmOGkt5BhXb83gy4+dVq5Oz3lbdrugvgjPQkf7UaM+PHgPA7uldcTyrIfcMU6gNWVvfFUjfBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:46.008503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.6282","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d66017ab43854d8162aa141ae4a5859c5c391269e8e785fdd51fd4df5e3b9f8","sha256:542c2ab07772c4a9ee37e1ab65a9011ab5c92f3454cd175a1334ab29ae428bc1"],"state_sha256":"569412efe4f3c97a065f039c29d0818dacdf3d7bbdbb54be2f1087b5e5ba34ae"}