{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZAVE2SYEU4OJR4IFCFQL64URDG","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":"43f68ea3f4de436af07e0627e6ff870314b7d9a41d87eb6b48ecfdc51ab9e75a","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-12T12:20:13Z","title_canon_sha256":"614f60eb5c66359d96b99df7204c1c52c185745dbb1f7dcff122742cbf66026b"},"schema_version":"1.0","source":{"id":"0908.1688","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1688","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1688v2","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1688","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZAVE2SYEU4OJ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"ZAVE2SYEU4OJR4IF","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"ZAVE2SYE","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:f91da6b5e96198968936ecb71dc82e632881cf88b83b5fc08af17edfa0185e49","target":"graph","created_at":"2026-05-18T00:05:15Z","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":"It is shown that a complex normal projective variety has non-positive Kodaira dimension if it admits a non-isomorphic quasi-polarized endomorphism. The geometric structure of the variety is described by methods of equivariant lifting and fibrations. (For endomorphisms of projective spaces, see version 1).","authors_text":"De-Qi Zhang, Noboru Nakayama","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-12T12:20:13Z","title":"Polarized endomorphisms of complex normal varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1688","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":"sha256:4ca19d2a0980bd824d0fa79adb62036477672c1e1d80a6f0db70f2f6d2b9b7ef","target":"record","created_at":"2026-05-18T00:05:15Z","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":"43f68ea3f4de436af07e0627e6ff870314b7d9a41d87eb6b48ecfdc51ab9e75a","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-12T12:20:13Z","title_canon_sha256":"614f60eb5c66359d96b99df7204c1c52c185745dbb1f7dcff122742cbf66026b"},"schema_version":"1.0","source":{"id":"0908.1688","kind":"arxiv","version":2}},"canonical_sha256":"c82a4d4b04a71c98f1051160bf7291198fd962ef51a0e6000e9a5fd59c2aa686","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c82a4d4b04a71c98f1051160bf7291198fd962ef51a0e6000e9a5fd59c2aa686","first_computed_at":"2026-05-18T00:05:15.142699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:15.142699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/37XKH3K1B1849kyUbivmuc0OaTVSfZr3EYt29mIGH2COqgBfOLQPlh5Y1UB0QzDUPZC6mQKJE4jmHFIOinWDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:15.143335Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.1688","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ca19d2a0980bd824d0fa79adb62036477672c1e1d80a6f0db70f2f6d2b9b7ef","sha256:f91da6b5e96198968936ecb71dc82e632881cf88b83b5fc08af17edfa0185e49"],"state_sha256":"dbd392e6aa0c9b50e9f5982f480a642f693c1d080ef41dd36bc273bcdea1990f"}