{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:NEWFZI7IJKYJHNTQTCWGLLBKIV","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":"b4520c4970f894125b8fa3bb346caab6ffe1a685d1b451a7f282b43fd1e43fc2","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2005-10-08T17:49:48Z","title_canon_sha256":"b8837b52f9b677633273d17ccffa3c447da3838ed8baa290b93c311a72b92d4a"},"schema_version":"1.0","source":{"id":"math/0510168","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0510168","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"math/0510168v1","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510168","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"NEWFZI7IJKYJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"NEWFZI7IJKYJHNTQ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"NEWFZI7I","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:334511e218d7195f9127f48d59e04ac719a9c8e525b107cd244a4b0ddbb8e236","target":"graph","created_at":"2026-05-18T01:38:24Z","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 complete the study of birational geometry of Fano fiber spaces $\\pi\\colon V\\to {\\mathbb P}^1$, the fiber of which is a Fano double hypersurface of index 1. For each family of these varieties we either prove birational rigidity or produce explicitly non-trivial structures of Fano fiber spaces. A new linear method of studying movable systems on Fano fiber spaces $V/{\\mathbb P}^1$ is developed.","authors_text":"Aleksandr V. Pukhlikov","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2005-10-08T17:49:48Z","title":"Birationally rigid varieties with a pencil of Fano double covers. III"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510168","kind":"arxiv","version":1},"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:b3659b888aafb0247a1591cce08e1bd2ce3ccc5ecdfb51d1ea42f51706ab29f9","target":"record","created_at":"2026-05-18T01:38:24Z","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":"b4520c4970f894125b8fa3bb346caab6ffe1a685d1b451a7f282b43fd1e43fc2","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2005-10-08T17:49:48Z","title_canon_sha256":"b8837b52f9b677633273d17ccffa3c447da3838ed8baa290b93c311a72b92d4a"},"schema_version":"1.0","source":{"id":"math/0510168","kind":"arxiv","version":1}},"canonical_sha256":"692c5ca3e84ab093b67098ac65ac2a456e7a6564a32f77e8807fd3d7d69dda4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"692c5ca3e84ab093b67098ac65ac2a456e7a6564a32f77e8807fd3d7d69dda4d","first_computed_at":"2026-05-18T01:38:24.754282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:24.754282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bc8cG2KdlVhygBkp0piIRIA0rTZnCdTmdieljOg3o6MdzBZbZGfTCrkO+Gik5dH2GgjJfqvzH4yoyHUkpS3JDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:24.754941Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0510168","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3659b888aafb0247a1591cce08e1bd2ce3ccc5ecdfb51d1ea42f51706ab29f9","sha256:334511e218d7195f9127f48d59e04ac719a9c8e525b107cd244a4b0ddbb8e236"],"state_sha256":"ccf345333464716b92f9ea580b2aaa56e70d718eacb04c33e91a70a1ead38ea2"}