{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WAXUYYWC5XWQY3VFBFD6IWQO2X","short_pith_number":"pith:WAXUYYWC","schema_version":"1.0","canonical_sha256":"b02f4c62c2eded0c6ea50947e45a0ed5c940656d21548c241a09f1707a3e9479","source":{"kind":"arxiv","id":"1702.08508","version":3},"attestation_state":"computed","paper":{"title":"Geometric Manin's Conjecture and rational curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Brian Lehmann, Sho Tanimoto","submitted_at":"2017-02-27T20:10:15Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.08508","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-02-27T20:10:15Z","cross_cats_sorted":[],"title_canon_sha256":"46ea152b7cc7d65cd3384bf8100e8b352c96255515f76150f931ac3292a164f4","abstract_canon_sha256":"2146a331a4b35b952eb11cfabadae9ee7ae748d956628f4a922accf6ae5315ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:24.000781Z","signature_b64":"9ykyUnP+Q9YUk6inWMh4Gup3YwQGX0Iew90vtYKD7EpIL/WlFTlHParMoGspx80YcNhyW/LXoFAhGpSXdibADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b02f4c62c2eded0c6ea50947e45a0ed5c940656d21548c241a09f1707a3e9479","last_reissued_at":"2026-05-17T23:48:24.000146Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:24.000146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric Manin's Conjecture and rational curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Brian Lehmann, Sho Tanimoto","submitted_at":"2017-02-27T20:10:15Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08508","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1702.08508","created_at":"2026-05-17T23:48:24.000237+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.08508v3","created_at":"2026-05-17T23:48:24.000237+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08508","created_at":"2026-05-17T23:48:24.000237+00:00"},{"alias_kind":"pith_short_12","alias_value":"WAXUYYWC5XWQ","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WAXUYYWC5XWQY3VF","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WAXUYYWC","created_at":"2026-05-18T12:31:53.515858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WAXUYYWC5XWQY3VFBFD6IWQO2X","json":"https://pith.science/pith/WAXUYYWC5XWQY3VFBFD6IWQO2X.json","graph_json":"https://pith.science/api/pith-number/WAXUYYWC5XWQY3VFBFD6IWQO2X/graph.json","events_json":"https://pith.science/api/pith-number/WAXUYYWC5XWQY3VFBFD6IWQO2X/events.json","paper":"https://pith.science/paper/WAXUYYWC"},"agent_actions":{"view_html":"https://pith.science/pith/WAXUYYWC5XWQY3VFBFD6IWQO2X","download_json":"https://pith.science/pith/WAXUYYWC5XWQY3VFBFD6IWQO2X.json","view_paper":"https://pith.science/paper/WAXUYYWC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.08508&json=true","fetch_graph":"https://pith.science/api/pith-number/WAXUYYWC5XWQY3VFBFD6IWQO2X/graph.json","fetch_events":"https://pith.science/api/pith-number/WAXUYYWC5XWQY3VFBFD6IWQO2X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WAXUYYWC5XWQY3VFBFD6IWQO2X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WAXUYYWC5XWQY3VFBFD6IWQO2X/action/storage_attestation","attest_author":"https://pith.science/pith/WAXUYYWC5XWQY3VFBFD6IWQO2X/action/author_attestation","sign_citation":"https://pith.science/pith/WAXUYYWC5XWQY3VFBFD6IWQO2X/action/citation_signature","submit_replication":"https://pith.science/pith/WAXUYYWC5XWQY3VFBFD6IWQO2X/action/replication_record"}},"created_at":"2026-05-17T23:48:24.000237+00:00","updated_at":"2026-05-17T23:48:24.000237+00:00"}