{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:54FSRD5IJW73GIQDM25WXWBWDP","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":"0ed6578f7501ca5afd864da8f0f221b48d185fd77a54a53663436a5a0c8b0d18","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-03-06T17:03:52Z","title_canon_sha256":"832604570361657600005249f1669130456f6b1bd1d3dccb6a9e2d4c0ded102a"},"schema_version":"1.0","source":{"id":"0903.1256","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.1256","created_at":"2026-05-17T23:53:20Z"},{"alias_kind":"arxiv_version","alias_value":"0903.1256v1","created_at":"2026-05-17T23:53:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.1256","created_at":"2026-05-17T23:53:20Z"},{"alias_kind":"pith_short_12","alias_value":"54FSRD5IJW73","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"54FSRD5IJW73GIQD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"54FSRD5I","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:4801e2827bc4ed68986157d03008bb855111c7e9c56ae9ac96749f327be8227a","target":"graph","created_at":"2026-05-17T23:53:20Z","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 show that polarized endomorphisms of rationally connected threefolds with at worst terminal singularities are equivariantly built up from those on Q-Fano threefolds, Gorenstein log del Pezzo surfaces and P^1. Similar results are obtained for polarized endomorphisms of uniruled threefolds and fourfolds. As a consequence, we show that every smooth Fano threefold with a polarized endomorphism of degree > 1, is rational.","authors_text":"De-Qi Zhang","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-03-06T17:03:52Z","title":"Polarized endomorphisms of uniruled varieties (with Appendix by Y. Fujimoto and N. Nakayama)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1256","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":"sha256:2e3fdbed0fd04b9dbfeec2445d8ddc740b8c3bb6cd901275e19a05a5faa15dd1","target":"record","created_at":"2026-05-17T23:53:20Z","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":"0ed6578f7501ca5afd864da8f0f221b48d185fd77a54a53663436a5a0c8b0d18","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-03-06T17:03:52Z","title_canon_sha256":"832604570361657600005249f1669130456f6b1bd1d3dccb6a9e2d4c0ded102a"},"schema_version":"1.0","source":{"id":"0903.1256","kind":"arxiv","version":1}},"canonical_sha256":"ef0b288fa84dbfb3220366bb6bd8361bfbf8a4fd8c1436b836f3721255acc175","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef0b288fa84dbfb3220366bb6bd8361bfbf8a4fd8c1436b836f3721255acc175","first_computed_at":"2026-05-17T23:53:20.050597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:20.050597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nTWRDDTw4SFnFr2hmWafQNiTiUAAGX32TO6JgD92vnuv2a3je650XJ+sYbsuQYsq32rGvoJPG7Kt9pQdkbFFAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:20.051098Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.1256","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e3fdbed0fd04b9dbfeec2445d8ddc740b8c3bb6cd901275e19a05a5faa15dd1","sha256:4801e2827bc4ed68986157d03008bb855111c7e9c56ae9ac96749f327be8227a"],"state_sha256":"a8e73d45400dffcdad31f3897903d652ac1f9cd560999ee1ca4a15819144c917"}