{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DZ544NTKGFJ6L3O42MZUDSEFQJ","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":"9ec6e41013ee96782182f7f1ec6240ef4a0543381e824ea7b046f8ed3f94546b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-19T23:32:47Z","title_canon_sha256":"50b70e25cac842a328ed56d93b5fc85eb7c3248ba9b4bb21e00132f3f1ff58b4"},"schema_version":"1.0","source":{"id":"1101.3797","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3797","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3797v1","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3797","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"DZ544NTKGFJ6","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DZ544NTKGFJ6L3O4","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DZ544NTK","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:49bd9818c3bae3b6f9aa44d2563127c800cb23c7eb52cbc6fd03406bdb4fb43b","target":"graph","created_at":"2026-05-17T23:53:36Z","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 prove that the space of smooth rational curves of degree $e$ in a general complete intersection of multidegree $(d_1, ..., d_m)$ in $\\PP^n$ is irreducible of the expected dimension if $\\sum_{i=1}^m d_i <\\frac{2n}{3}$ and $n$ is large enough. This generalizes the results of Harris, Roth and Starr \\cite{hrs}, and is achieved by proving that the space of conics passing through any point of a general complete intersection has constant dimension if $\\sum_{i=1}^m d_i$ is small compared to $n$.","authors_text":"N. Mohan Kumar, Roya Beheshti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-19T23:32:47Z","title":"Spaces of rational curves in complete intersections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3797","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":"sha256:2c68068848c1d8167aa0884c5907a633b2b9740175c5eaef84a367eeb64c3908","target":"record","created_at":"2026-05-17T23:53:36Z","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":"9ec6e41013ee96782182f7f1ec6240ef4a0543381e824ea7b046f8ed3f94546b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-19T23:32:47Z","title_canon_sha256":"50b70e25cac842a328ed56d93b5fc85eb7c3248ba9b4bb21e00132f3f1ff58b4"},"schema_version":"1.0","source":{"id":"1101.3797","kind":"arxiv","version":1}},"canonical_sha256":"1e7bce366a3153e5eddcd33341c885825936a8ca6caf8fdcf13cdcb603729ff3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e7bce366a3153e5eddcd33341c885825936a8ca6caf8fdcf13cdcb603729ff3","first_computed_at":"2026-05-17T23:53:36.754738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:36.754738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jQcsid9rhOwxS/NWK25S+a5p21XnPDnL52sECq4K86IJ677/2MD8oQTHRTvk3oDs8qMy+5lrGzIkleRPTBZ9Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:36.755641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3797","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c68068848c1d8167aa0884c5907a633b2b9740175c5eaef84a367eeb64c3908","sha256:49bd9818c3bae3b6f9aa44d2563127c800cb23c7eb52cbc6fd03406bdb4fb43b"],"state_sha256":"b8d20e60758baffd0b30395ddc4f5a9d3dd8f51176315790dd2b1420d4485963"}