{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:F4HZWN7HZPQ7ZV76MFPP7G6DUT","short_pith_number":"pith:F4HZWN7H","schema_version":"1.0","canonical_sha256":"2f0f9b37e7cbe1fcd7fe615eff9bc3a4f01d6e40418d118ab3167eb59540bb34","source":{"kind":"arxiv","id":"1310.2572","version":2},"attestation_state":"computed","paper":{"title":"Birational geometry of Fano hypersurfaces of index two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Aleksandr Pukhlikov","submitted_at":"2013-10-09T18:35:57Z","abstract_excerpt":"We prove that every non-trivial structure of a rationally connected fibre space (and so every structure of a Mori-Fano fibre space) on a general (in the sense of Zariski topology) hypersurface of degree $M$ in the $(M+1)$-dimensional projective space for $M\\geq 14$ is given by a pencil of hyperplane sections. In particular, the variety $V$ is non-rational and its group of birational self-maps coincide with the group of biregular automorphisms and is therefore trivial. The proof is based on the techniques of the method of maximal singularities and the inversion of adjunction."},"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":"1310.2572","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-09T18:35:57Z","cross_cats_sorted":[],"title_canon_sha256":"90449e9fbd8a5e3f7673962789f4b346d1571ec3e99cae742427dd81ac843343","abstract_canon_sha256":"3bf50bb634979a31a2093949f49e09b0e051202b82e1b27a8978e90ee4a07d4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:13.813350Z","signature_b64":"g31IFMRnJnQjxs5Ab/rhJMXbsKtuA/NkoBweQTeBc/LoB4hLd6bPZSv5wOKJQZH8YRICfcoeo3UgkUd/2HqkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f0f9b37e7cbe1fcd7fe615eff9bc3a4f01d6e40418d118ab3167eb59540bb34","last_reissued_at":"2026-05-18T03:07:13.812747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:13.812747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Birational geometry of Fano hypersurfaces of index two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Aleksandr Pukhlikov","submitted_at":"2013-10-09T18:35:57Z","abstract_excerpt":"We prove that every non-trivial structure of a rationally connected fibre space (and so every structure of a Mori-Fano fibre space) on a general (in the sense of Zariski topology) hypersurface of degree $M$ in the $(M+1)$-dimensional projective space for $M\\geq 14$ is given by a pencil of hyperplane sections. In particular, the variety $V$ is non-rational and its group of birational self-maps coincide with the group of biregular automorphisms and is therefore trivial. The proof is based on the techniques of the method of maximal singularities and the inversion of adjunction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2572","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":"1310.2572","created_at":"2026-05-18T03:07:13.812831+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.2572v2","created_at":"2026-05-18T03:07:13.812831+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2572","created_at":"2026-05-18T03:07:13.812831+00:00"},{"alias_kind":"pith_short_12","alias_value":"F4HZWN7HZPQ7","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"F4HZWN7HZPQ7ZV76","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"F4HZWN7H","created_at":"2026-05-18T12:27:43.054852+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/F4HZWN7HZPQ7ZV76MFPP7G6DUT","json":"https://pith.science/pith/F4HZWN7HZPQ7ZV76MFPP7G6DUT.json","graph_json":"https://pith.science/api/pith-number/F4HZWN7HZPQ7ZV76MFPP7G6DUT/graph.json","events_json":"https://pith.science/api/pith-number/F4HZWN7HZPQ7ZV76MFPP7G6DUT/events.json","paper":"https://pith.science/paper/F4HZWN7H"},"agent_actions":{"view_html":"https://pith.science/pith/F4HZWN7HZPQ7ZV76MFPP7G6DUT","download_json":"https://pith.science/pith/F4HZWN7HZPQ7ZV76MFPP7G6DUT.json","view_paper":"https://pith.science/paper/F4HZWN7H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.2572&json=true","fetch_graph":"https://pith.science/api/pith-number/F4HZWN7HZPQ7ZV76MFPP7G6DUT/graph.json","fetch_events":"https://pith.science/api/pith-number/F4HZWN7HZPQ7ZV76MFPP7G6DUT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F4HZWN7HZPQ7ZV76MFPP7G6DUT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F4HZWN7HZPQ7ZV76MFPP7G6DUT/action/storage_attestation","attest_author":"https://pith.science/pith/F4HZWN7HZPQ7ZV76MFPP7G6DUT/action/author_attestation","sign_citation":"https://pith.science/pith/F4HZWN7HZPQ7ZV76MFPP7G6DUT/action/citation_signature","submit_replication":"https://pith.science/pith/F4HZWN7HZPQ7ZV76MFPP7G6DUT/action/replication_record"}},"created_at":"2026-05-18T03:07:13.812831+00:00","updated_at":"2026-05-18T03:07:13.812831+00:00"}