{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:I2TLJX44BGGHZMCQJV77Q7MZC7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6a8d9cfca640d3fed1113ff9ed1a4a6f86aea7bf0a0a12d3830f6997aa93f849","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2002-01-30T18:47:24Z","title_canon_sha256":"925e41fc971fedc571c510f671bf435c36eab6f90ab8ecef92c611c2c9a62f84"},"schema_version":"1.0","source":{"id":"math/0201302","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0201302","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0201302v2","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0201302","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"I2TLJX44BGGH","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"I2TLJX44BGGHZMCQ","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"I2TLJX44","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:c7816e26c18b5227b1f7ab0d6917346c637d6f23d29ea004c7a7f70e98dee9ad","target":"graph","created_at":"2026-05-18T01:38:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that a smooth Fano hypersurface $V=V_M\\subset{\\Bbb P}^M$, $M\\geq 6$, is birationally superrigid. In particular, it cannot be fibered into uniruled varieties by a non-trivial rational map and each birational map onto a minimal Fano variety of the same dimension is a biregular isomorphism. The proof is based on the method of maximal singularities combined with the connectedness principle of Shokurov and Koll\\' ar.","authors_text":"Aleksandr V. Pukhlikov","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2002-01-30T18:47:24Z","title":"Birationally rigid Fano hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0201302","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0d1b9c1635ad12fdd286ef365f39be079216c9827c9b7d3aadd610ef694c1ab0","target":"record","created_at":"2026-05-18T01:38:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6a8d9cfca640d3fed1113ff9ed1a4a6f86aea7bf0a0a12d3830f6997aa93f849","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2002-01-30T18:47:24Z","title_canon_sha256":"925e41fc971fedc571c510f671bf435c36eab6f90ab8ecef92c611c2c9a62f84"},"schema_version":"1.0","source":{"id":"math/0201302","kind":"arxiv","version":2}},"canonical_sha256":"46a6b4df9c098c7cb0504d7ff87d9917df9581ab3e47d1e8513dc7526ead2b31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46a6b4df9c098c7cb0504d7ff87d9917df9581ab3e47d1e8513dc7526ead2b31","first_computed_at":"2026-05-18T01:38:29.692413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:29.692413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e2FuoxlVlRCkNO4ND7NAuChk+f34zLfwIatEh8SiU33iBIiAqTb21T8z1+bEow/KTJ9w3fO0kh3WPWqG72kfAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:29.692779Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0201302","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d1b9c1635ad12fdd286ef365f39be079216c9827c9b7d3aadd610ef694c1ab0","sha256:c7816e26c18b5227b1f7ab0d6917346c637d6f23d29ea004c7a7f70e98dee9ad"],"state_sha256":"47c67d87f4a89e5644f4a57b78759e2fea2472ea1d3197c96d0b3b226239fcb3"}