{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FNZZ7DM6I3NS5LKEUFIJFYWDY4","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":"31caa32cf47668f59bb64b4981f501182bfdd18b66ba2145d264b334f42e0e5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-14T10:43:11Z","title_canon_sha256":"9348ae8521f0968a70cc4208ec3ffc0730b8304c2035a0faad4bf8debc48b747"},"schema_version":"1.0","source":{"id":"1108.2860","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2860","created_at":"2026-05-18T04:14:56Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2860v2","created_at":"2026-05-18T04:14:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2860","created_at":"2026-05-18T04:14:56Z"},{"alias_kind":"pith_short_12","alias_value":"FNZZ7DM6I3NS","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FNZZ7DM6I3NS5LKE","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FNZZ7DM6","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:2cb053dd1993823317cd8681aab51aa89d8fe800d00442f1501bb7e11c4c99f5","target":"graph","created_at":"2026-05-18T04:14:56Z","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":"Using ideas from the theory of tropical curves and degeneration, we prove that any Fano hypersurface (and more generally Fano complete intersections) is swept by at most quadratic rational curves.","authors_text":"Takeo Nishinou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-14T10:43:11Z","title":"Rational curves in Fano hypersurfaces and tropical curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2860","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":"sha256:1e9c42960ea07c8b664b685ffaa419aa5b3be7e13df5f5a7e539e1482b8cdac5","target":"record","created_at":"2026-05-18T04:14:56Z","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":"31caa32cf47668f59bb64b4981f501182bfdd18b66ba2145d264b334f42e0e5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-14T10:43:11Z","title_canon_sha256":"9348ae8521f0968a70cc4208ec3ffc0730b8304c2035a0faad4bf8debc48b747"},"schema_version":"1.0","source":{"id":"1108.2860","kind":"arxiv","version":2}},"canonical_sha256":"2b739f8d9e46db2ead44a15092e2c3c7119743d960c48f35259d4480bca495ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b739f8d9e46db2ead44a15092e2c3c7119743d960c48f35259d4480bca495ae","first_computed_at":"2026-05-18T04:14:56.352212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:56.352212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s3EdNOaa3P61xYXnvj6GCGzGV3XwFhjog4LiXVGbrmQGf+1kR6ey3Xh5zUPt+InBx6RHEM05EGT6JH/WWUmzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:56.352675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2860","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e9c42960ea07c8b664b685ffaa419aa5b3be7e13df5f5a7e539e1482b8cdac5","sha256:2cb053dd1993823317cd8681aab51aa89d8fe800d00442f1501bb7e11c4c99f5"],"state_sha256":"f6fb9150e413f22ccaf4cbaa95cc3d874abc5824432dfb4c0a13d88f6459fbc0"}