{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UBC7J5I73KDNT45HQPVLT4AXW5","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":"2d196b36289472a5a2ca61f144441a614afe42a4984619476349f882c46df751","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-06-17T07:37:50Z","title_canon_sha256":"7a682bcccb5b38b91d9d4ef0a3f2e24138bacee2d84e54a60ff00681bc2553a7"},"schema_version":"1.0","source":{"id":"2506.14274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.14274","created_at":"2026-07-05T11:22:52Z"},{"alias_kind":"arxiv_version","alias_value":"2506.14274v1","created_at":"2026-07-05T11:22:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.14274","created_at":"2026-07-05T11:22:52Z"},{"alias_kind":"pith_short_12","alias_value":"UBC7J5I73KDN","created_at":"2026-07-05T11:22:52Z"},{"alias_kind":"pith_short_16","alias_value":"UBC7J5I73KDNT45H","created_at":"2026-07-05T11:22:52Z"},{"alias_kind":"pith_short_8","alias_value":"UBC7J5I7","created_at":"2026-07-05T11:22:52Z"}],"graph_snapshots":[{"event_id":"sha256:100c9a0bbb0481afd559a731aaf554770bb98e21b9eb99b30a644245345c434e","target":"graph","created_at":"2026-07-05T11:22:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.14274/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that a smooth rationally connected projective threefold of Picard number two is toric if and only if it admits an int-amplified endomorphism. As a corollary, we show that a totally invariant smooth curve of a non-isomorphic surjective endomorphism of $\\mathbb{P}^3$ must be a line when it is blowup-equivariant.","authors_text":"Guolei Zhong, Sheng Meng, Zelong Chen","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-06-17T07:37:50Z","title":"On smooth rationally connected projective threefolds of Picard number two admitting int-amplified endomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.14274","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:fca5f89cb8f1862bc66de47154e2e28738ee603aa197ac7f23a6a64e5332d390","target":"record","created_at":"2026-07-05T11:22:52Z","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":"2d196b36289472a5a2ca61f144441a614afe42a4984619476349f882c46df751","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-06-17T07:37:50Z","title_canon_sha256":"7a682bcccb5b38b91d9d4ef0a3f2e24138bacee2d84e54a60ff00681bc2553a7"},"schema_version":"1.0","source":{"id":"2506.14274","kind":"arxiv","version":1}},"canonical_sha256":"a045f4f51fda86d9f3a783eab9f017b77e749ef9d088df1d6596e7a0eab8906a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a045f4f51fda86d9f3a783eab9f017b77e749ef9d088df1d6596e7a0eab8906a","first_computed_at":"2026-07-05T11:22:52.436304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:22:52.436304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3z6eUlL8WfPJRHFNjqLZ+rkYqE8ocL/mUAHt7QR/bOTDA/QViYC6YvUIW1XGx/OVrlcCHVO8Xx8abKSNxKBdCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:22:52.436789Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.14274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fca5f89cb8f1862bc66de47154e2e28738ee603aa197ac7f23a6a64e5332d390","sha256:100c9a0bbb0481afd559a731aaf554770bb98e21b9eb99b30a644245345c434e"],"state_sha256":"abfc9e6788654d4dd27ae9ca94f9b19b4f87ef0540f6e3534aabff13eeb164d2"}