{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:F4HZWN7HZPQ7ZV76MFPP7G6DUT","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":"3bf50bb634979a31a2093949f49e09b0e051202b82e1b27a8978e90ee4a07d4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-09T18:35:57Z","title_canon_sha256":"90449e9fbd8a5e3f7673962789f4b346d1571ec3e99cae742427dd81ac843343"},"schema_version":"1.0","source":{"id":"1310.2572","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2572","created_at":"2026-05-18T03:07:13Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2572v2","created_at":"2026-05-18T03:07:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2572","created_at":"2026-05-18T03:07:13Z"},{"alias_kind":"pith_short_12","alias_value":"F4HZWN7HZPQ7","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"F4HZWN7HZPQ7ZV76","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"F4HZWN7H","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:1d069544d897a015337bda63ccc9ebbb3da9a8a47952fcb7b22cf5bb4979dd93","target":"graph","created_at":"2026-05-18T03:07:13Z","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 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.","authors_text":"Aleksandr Pukhlikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-09T18:35:57Z","title":"Birational geometry of Fano hypersurfaces of index two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2572","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":"sha256:486e6e90d0c9988bd9c17617ae0c212dd41384cdbbc548064e0349cbf182b8e6","target":"record","created_at":"2026-05-18T03:07:13Z","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":"3bf50bb634979a31a2093949f49e09b0e051202b82e1b27a8978e90ee4a07d4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-09T18:35:57Z","title_canon_sha256":"90449e9fbd8a5e3f7673962789f4b346d1571ec3e99cae742427dd81ac843343"},"schema_version":"1.0","source":{"id":"1310.2572","kind":"arxiv","version":2}},"canonical_sha256":"2f0f9b37e7cbe1fcd7fe615eff9bc3a4f01d6e40418d118ab3167eb59540bb34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f0f9b37e7cbe1fcd7fe615eff9bc3a4f01d6e40418d118ab3167eb59540bb34","first_computed_at":"2026-05-18T03:07:13.812747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:13.812747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g31IFMRnJnQjxs5Ab/rhJMXbsKtuA/NkoBweQTeBc/LoB4hLd6bPZSv5wOKJQZH8YRICfcoeo3UgkUd/2HqkDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:13.813350Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.2572","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:486e6e90d0c9988bd9c17617ae0c212dd41384cdbbc548064e0349cbf182b8e6","sha256:1d069544d897a015337bda63ccc9ebbb3da9a8a47952fcb7b22cf5bb4979dd93"],"state_sha256":"cb305d2f6bec67abb1067932b4452e2d2c7832f92a49d008f93d8e6969b65d76"}