{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4JJ2NZTBK5A5FDWKSTHCS2I2KO","short_pith_number":"pith:4JJ2NZTB","schema_version":"1.0","canonical_sha256":"e253a6e6615741d28eca94ce29691a539bf33ec3cd14cb37695f05973e8975e9","source":{"kind":"arxiv","id":"1705.02931","version":3},"attestation_state":"computed","paper":{"title":"Rationality proofs by curve counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Anton Mellit","submitted_at":"2017-05-08T15:54:10Z","abstract_excerpt":"We propose an approach for showing rationality of an algebraic variety $X$. We try to cover $X$ by rational curves of certain type and count how many curves pass through a generic point. If the answer is $1$, then we can sometimes reduce the question of rationality of $X$ to the question of rationality of a closed subvariety of $X$. This approach is applied to the case of the so-called Ueno-Campana manifolds. Our experiments indicate that the previously open cases $X_{4,6}$ and $X_{5,6}$ are both rational. However, this result is not rigorously justified and depends on a heuristic argument and"},"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":"1705.02931","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-08T15:54:10Z","cross_cats_sorted":[],"title_canon_sha256":"b268bfac2e2db95229f5c9f6fa459550e2c103c1a7a4b3b64cf3e740c7f8f8b1","abstract_canon_sha256":"96f08b1bce829dc7c2796eb0867994b89942f14b380d22671bd60eb74a7e472a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:50.272839Z","signature_b64":"5wPNGxZBrTv+pHmSgzdTmxP/Oo+9fhgZOaR/bGF1bNWad5wfrWCc5yaeSC1HRJ/W8Qbt1NxwqxK3ygT1IoHRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e253a6e6615741d28eca94ce29691a539bf33ec3cd14cb37695f05973e8975e9","last_reissued_at":"2026-05-17T23:58:50.272373Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:50.272373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rationality proofs by curve counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Anton Mellit","submitted_at":"2017-05-08T15:54:10Z","abstract_excerpt":"We propose an approach for showing rationality of an algebraic variety $X$. We try to cover $X$ by rational curves of certain type and count how many curves pass through a generic point. If the answer is $1$, then we can sometimes reduce the question of rationality of $X$ to the question of rationality of a closed subvariety of $X$. This approach is applied to the case of the so-called Ueno-Campana manifolds. Our experiments indicate that the previously open cases $X_{4,6}$ and $X_{5,6}$ are both rational. However, this result is not rigorously justified and depends on a heuristic argument and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02931","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":"1705.02931","created_at":"2026-05-17T23:58:50.272439+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.02931v3","created_at":"2026-05-17T23:58:50.272439+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02931","created_at":"2026-05-17T23:58:50.272439+00:00"},{"alias_kind":"pith_short_12","alias_value":"4JJ2NZTBK5A5","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"4JJ2NZTBK5A5FDWK","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"4JJ2NZTB","created_at":"2026-05-18T12:31:00.734936+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/4JJ2NZTBK5A5FDWKSTHCS2I2KO","json":"https://pith.science/pith/4JJ2NZTBK5A5FDWKSTHCS2I2KO.json","graph_json":"https://pith.science/api/pith-number/4JJ2NZTBK5A5FDWKSTHCS2I2KO/graph.json","events_json":"https://pith.science/api/pith-number/4JJ2NZTBK5A5FDWKSTHCS2I2KO/events.json","paper":"https://pith.science/paper/4JJ2NZTB"},"agent_actions":{"view_html":"https://pith.science/pith/4JJ2NZTBK5A5FDWKSTHCS2I2KO","download_json":"https://pith.science/pith/4JJ2NZTBK5A5FDWKSTHCS2I2KO.json","view_paper":"https://pith.science/paper/4JJ2NZTB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.02931&json=true","fetch_graph":"https://pith.science/api/pith-number/4JJ2NZTBK5A5FDWKSTHCS2I2KO/graph.json","fetch_events":"https://pith.science/api/pith-number/4JJ2NZTBK5A5FDWKSTHCS2I2KO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4JJ2NZTBK5A5FDWKSTHCS2I2KO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4JJ2NZTBK5A5FDWKSTHCS2I2KO/action/storage_attestation","attest_author":"https://pith.science/pith/4JJ2NZTBK5A5FDWKSTHCS2I2KO/action/author_attestation","sign_citation":"https://pith.science/pith/4JJ2NZTBK5A5FDWKSTHCS2I2KO/action/citation_signature","submit_replication":"https://pith.science/pith/4JJ2NZTBK5A5FDWKSTHCS2I2KO/action/replication_record"}},"created_at":"2026-05-17T23:58:50.272439+00:00","updated_at":"2026-05-17T23:58:50.272439+00:00"}