{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:TV5MZHGRXXVAAW5GDU6LN7AGAR","short_pith_number":"pith:TV5MZHGR","schema_version":"1.0","canonical_sha256":"9d7acc9cd1bdea005ba61d3cb6fc06046bdd632a938fd3566123d2a7ccb65851","source":{"kind":"arxiv","id":"1405.5154","version":2},"attestation_state":"computed","paper":{"title":"The Fano variety of lines and rationality problem for a cubic hypersurface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Evgeny Shinder, Sergey Galkin","submitted_at":"2014-05-20T17:00:27Z","abstract_excerpt":"We find a relation between a cubic hypersurface $Y$ and its Fano variety of lines $F(Y)$ in the Grothendieck ring of varieties. We prove that if the class of an affine line is not a zero-divisor in the Grothendieck ring of varieties, then Fano variety of lines on a smooth rational cubic fourfold is birational to a Hilbert scheme of two points on a K3 surface; in particular, general cubic fourfold is irrational."},"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":"1405.5154","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-20T17:00:27Z","cross_cats_sorted":[],"title_canon_sha256":"c68c7ce609f8fde9224ada1c2ee7222f580781affd87aa46e72224694186ecd8","abstract_canon_sha256":"7f4d3b38dcf6f61c16d80cf4957f60bf19374b249e2eea8ea9587391a7f00813"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:56.181748Z","signature_b64":"6OXM2KYG+jCpWhiTMI9Dd6pgPhtJvIi8ckJ3CnWq5583oaAS4KRcmLe2UXIgTFifG25GdlzXX1+tlmCA3nRzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d7acc9cd1bdea005ba61d3cb6fc06046bdd632a938fd3566123d2a7ccb65851","last_reissued_at":"2026-05-18T02:48:56.181145Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:56.181145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Fano variety of lines and rationality problem for a cubic hypersurface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Evgeny Shinder, Sergey Galkin","submitted_at":"2014-05-20T17:00:27Z","abstract_excerpt":"We find a relation between a cubic hypersurface $Y$ and its Fano variety of lines $F(Y)$ in the Grothendieck ring of varieties. We prove that if the class of an affine line is not a zero-divisor in the Grothendieck ring of varieties, then Fano variety of lines on a smooth rational cubic fourfold is birational to a Hilbert scheme of two points on a K3 surface; in particular, general cubic fourfold is irrational."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5154","kind":"arxiv","version":2},"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":"1405.5154","created_at":"2026-05-18T02:48:56.181236+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.5154v2","created_at":"2026-05-18T02:48:56.181236+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5154","created_at":"2026-05-18T02:48:56.181236+00:00"},{"alias_kind":"pith_short_12","alias_value":"TV5MZHGRXXVA","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"TV5MZHGRXXVAAW5G","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"TV5MZHGR","created_at":"2026-05-18T12:28:52.271510+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.18104","citing_title":"Zeta functions of K3 categories over finite fields","ref_index":23,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TV5MZHGRXXVAAW5GDU6LN7AGAR","json":"https://pith.science/pith/TV5MZHGRXXVAAW5GDU6LN7AGAR.json","graph_json":"https://pith.science/api/pith-number/TV5MZHGRXXVAAW5GDU6LN7AGAR/graph.json","events_json":"https://pith.science/api/pith-number/TV5MZHGRXXVAAW5GDU6LN7AGAR/events.json","paper":"https://pith.science/paper/TV5MZHGR"},"agent_actions":{"view_html":"https://pith.science/pith/TV5MZHGRXXVAAW5GDU6LN7AGAR","download_json":"https://pith.science/pith/TV5MZHGRXXVAAW5GDU6LN7AGAR.json","view_paper":"https://pith.science/paper/TV5MZHGR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.5154&json=true","fetch_graph":"https://pith.science/api/pith-number/TV5MZHGRXXVAAW5GDU6LN7AGAR/graph.json","fetch_events":"https://pith.science/api/pith-number/TV5MZHGRXXVAAW5GDU6LN7AGAR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TV5MZHGRXXVAAW5GDU6LN7AGAR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TV5MZHGRXXVAAW5GDU6LN7AGAR/action/storage_attestation","attest_author":"https://pith.science/pith/TV5MZHGRXXVAAW5GDU6LN7AGAR/action/author_attestation","sign_citation":"https://pith.science/pith/TV5MZHGRXXVAAW5GDU6LN7AGAR/action/citation_signature","submit_replication":"https://pith.science/pith/TV5MZHGRXXVAAW5GDU6LN7AGAR/action/replication_record"}},"created_at":"2026-05-18T02:48:56.181236+00:00","updated_at":"2026-05-18T02:48:56.181236+00:00"}