{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WAXUYYWC5XWQY3VFBFD6IWQO2X","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":"2146a331a4b35b952eb11cfabadae9ee7ae748d956628f4a922accf6ae5315ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-02-27T20:10:15Z","title_canon_sha256":"46ea152b7cc7d65cd3384bf8100e8b352c96255515f76150f931ac3292a164f4"},"schema_version":"1.0","source":{"id":"1702.08508","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08508","created_at":"2026-05-17T23:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08508v3","created_at":"2026-05-17T23:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08508","created_at":"2026-05-17T23:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"WAXUYYWC5XWQ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WAXUYYWC5XWQY3VF","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WAXUYYWC","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:d4758d24deeba553f9e112ca316b7a18c7f2bfae28cb06b85b3f7fba50aadc72","target":"graph","created_at":"2026-05-17T23:48:24Z","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 Fano variety over the complex numbers. We study the moduli spaces of rational curves on $X$ using the perspective of Manin's Conjecture. In particular, we bound the dimension and number of components of spaces of rational curves on $X$. We propose a Geometric Manin's Conjecture predicting the growth rate of a counting function associated to the irreducible components of these moduli spaces.","authors_text":"Brian Lehmann, Sho Tanimoto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-02-27T20:10:15Z","title":"Geometric Manin's Conjecture and rational curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08508","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:e05d1e5bb114df8e8ab6c5f24259542c66bb2eb6cf18b1452752b97c44047b31","target":"record","created_at":"2026-05-17T23:48:24Z","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":"2146a331a4b35b952eb11cfabadae9ee7ae748d956628f4a922accf6ae5315ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-02-27T20:10:15Z","title_canon_sha256":"46ea152b7cc7d65cd3384bf8100e8b352c96255515f76150f931ac3292a164f4"},"schema_version":"1.0","source":{"id":"1702.08508","kind":"arxiv","version":3}},"canonical_sha256":"b02f4c62c2eded0c6ea50947e45a0ed5c940656d21548c241a09f1707a3e9479","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b02f4c62c2eded0c6ea50947e45a0ed5c940656d21548c241a09f1707a3e9479","first_computed_at":"2026-05-17T23:48:24.000146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:24.000146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ykyUnP+Q9YUk6inWMh4Gup3YwQGX0Iew90vtYKD7EpIL/WlFTlHParMoGspx80YcNhyW/LXoFAhGpSXdibADA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:24.000781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.08508","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e05d1e5bb114df8e8ab6c5f24259542c66bb2eb6cf18b1452752b97c44047b31","sha256:d4758d24deeba553f9e112ca316b7a18c7f2bfae28cb06b85b3f7fba50aadc72"],"state_sha256":"f8dd17d64cab9bf1c81d30e539133908e3b337badde148b219b467e4e8bcdcbc"}