{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HUUHZYWY5N6RKMHVDXCMPQE3AX","short_pith_number":"pith:HUUHZYWY","schema_version":"1.0","canonical_sha256":"3d287ce2d8eb7d1530f51dc4c7c09b05f0cbc4687a4ecb3f0d92d4c35cf37ac5","source":{"kind":"arxiv","id":"1712.08796","version":1},"attestation_state":"computed","paper":{"title":"Birational geometry of singular Fano hypersurfaces of index two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Aleksandr V. Pukhlikov","submitted_at":"2017-12-23T16:02:32Z","abstract_excerpt":"For a Zariski general (regular) hypersurface $V$ of degree $M$ in the $(M+1)$-dimensional projective space, where $M$ is at least 16, with at most quadratic singularities of rank at least 13, we give a complete description of the structures of rationally connected (or Fano-Mori) fibre space: every such structure over a positive-dimensional base is a pencil of hyperplane sections. This implies, in particular, that $V$ is non-rational and its groups of birational and biregular automorphisms coincide. The set of non-regular hypersurfaces has codimension at least $\\frac12(M-11)(M-10)-10$ in the na"},"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":"1712.08796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-23T16:02:32Z","cross_cats_sorted":[],"title_canon_sha256":"63e76acfdf5be16c29760d8aff78ceacef98704f08ebf023193a8190bf0eb83e","abstract_canon_sha256":"6d1ebf92637969dc70fc81803d971f6fe9d88b5a40631d0ee32209252a2a7934"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:16.786393Z","signature_b64":"xC080GuHeQJQxw5Y/GGe1N1Uel2NEG4oj47eSviJP7aAPwBZ30nwU4uXMy3kRPqozer5mKqYnGZ+UATvDU4GDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d287ce2d8eb7d1530f51dc4c7c09b05f0cbc4687a4ecb3f0d92d4c35cf37ac5","last_reissued_at":"2026-05-18T00:27:16.785870Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:16.785870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Birational geometry of singular Fano hypersurfaces of index two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Aleksandr V. Pukhlikov","submitted_at":"2017-12-23T16:02:32Z","abstract_excerpt":"For a Zariski general (regular) hypersurface $V$ of degree $M$ in the $(M+1)$-dimensional projective space, where $M$ is at least 16, with at most quadratic singularities of rank at least 13, we give a complete description of the structures of rationally connected (or Fano-Mori) fibre space: every such structure over a positive-dimensional base is a pencil of hyperplane sections. This implies, in particular, that $V$ is non-rational and its groups of birational and biregular automorphisms coincide. The set of non-regular hypersurfaces has codimension at least $\\frac12(M-11)(M-10)-10$ in the na"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08796","kind":"arxiv","version":1},"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":"1712.08796","created_at":"2026-05-18T00:27:16.785948+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.08796v1","created_at":"2026-05-18T00:27:16.785948+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08796","created_at":"2026-05-18T00:27:16.785948+00:00"},{"alias_kind":"pith_short_12","alias_value":"HUUHZYWY5N6R","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"HUUHZYWY5N6RKMHV","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"HUUHZYWY","created_at":"2026-05-18T12:31:21.493067+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/HUUHZYWY5N6RKMHVDXCMPQE3AX","json":"https://pith.science/pith/HUUHZYWY5N6RKMHVDXCMPQE3AX.json","graph_json":"https://pith.science/api/pith-number/HUUHZYWY5N6RKMHVDXCMPQE3AX/graph.json","events_json":"https://pith.science/api/pith-number/HUUHZYWY5N6RKMHVDXCMPQE3AX/events.json","paper":"https://pith.science/paper/HUUHZYWY"},"agent_actions":{"view_html":"https://pith.science/pith/HUUHZYWY5N6RKMHVDXCMPQE3AX","download_json":"https://pith.science/pith/HUUHZYWY5N6RKMHVDXCMPQE3AX.json","view_paper":"https://pith.science/paper/HUUHZYWY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.08796&json=true","fetch_graph":"https://pith.science/api/pith-number/HUUHZYWY5N6RKMHVDXCMPQE3AX/graph.json","fetch_events":"https://pith.science/api/pith-number/HUUHZYWY5N6RKMHVDXCMPQE3AX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HUUHZYWY5N6RKMHVDXCMPQE3AX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HUUHZYWY5N6RKMHVDXCMPQE3AX/action/storage_attestation","attest_author":"https://pith.science/pith/HUUHZYWY5N6RKMHVDXCMPQE3AX/action/author_attestation","sign_citation":"https://pith.science/pith/HUUHZYWY5N6RKMHVDXCMPQE3AX/action/citation_signature","submit_replication":"https://pith.science/pith/HUUHZYWY5N6RKMHVDXCMPQE3AX/action/replication_record"}},"created_at":"2026-05-18T00:27:16.785948+00:00","updated_at":"2026-05-18T00:27:16.785948+00:00"}