{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:GI5PMAPZNB25O4WRR7WOPOEAT2","short_pith_number":"pith:GI5PMAPZ","schema_version":"1.0","canonical_sha256":"323af601f96875d772d18fece7b8809eb7709c544e7c8bf5d12ec0e91fed77c8","source":{"kind":"arxiv","id":"1106.1825","version":2},"attestation_state":"computed","paper":{"title":"Periodic points of birational maps on projective surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"Junyi Xie","submitted_at":"2011-06-09T14:06:47Z","abstract_excerpt":"We classify birational maps of projective smooth surfaces whose non-critical periodic points are Zariski dense. In particular, we show that if the first dynamical degree is greater than one, then the periodic points are Zariski dense."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1106.1825","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-09T14:06:47Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"d288d297ac538649e88a0036af08b3ef09c3dc14f950369884d50e422b6d9c4b","abstract_canon_sha256":"cba1b2390709a358dfe6e73bd57e4a297a75d4cbf715563048d54388d6fe6b8e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:21.961652Z","signature_b64":"UWA8RMVWxI+562k1zZjOpvI8NipKhH257pL0TQ99fivA4gikeP4AL2lFeNgK3IE/bgoZDKKoNTxLuO4fTS4WBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"323af601f96875d772d18fece7b8809eb7709c544e7c8bf5d12ec0e91fed77c8","last_reissued_at":"2026-05-18T01:28:21.961011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:21.961011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Periodic points of birational maps on projective surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"Junyi Xie","submitted_at":"2011-06-09T14:06:47Z","abstract_excerpt":"We classify birational maps of projective smooth surfaces whose non-critical periodic points are Zariski dense. In particular, we show that if the first dynamical degree is greater than one, then the periodic points are Zariski dense."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1825","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1106.1825","created_at":"2026-05-18T01:28:21.961095+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.1825v2","created_at":"2026-05-18T01:28:21.961095+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1825","created_at":"2026-05-18T01:28:21.961095+00:00"},{"alias_kind":"pith_short_12","alias_value":"GI5PMAPZNB25","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"GI5PMAPZNB25O4WR","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"GI5PMAPZ","created_at":"2026-05-18T12:26:30.835961+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GI5PMAPZNB25O4WRR7WOPOEAT2","json":"https://pith.science/pith/GI5PMAPZNB25O4WRR7WOPOEAT2.json","graph_json":"https://pith.science/api/pith-number/GI5PMAPZNB25O4WRR7WOPOEAT2/graph.json","events_json":"https://pith.science/api/pith-number/GI5PMAPZNB25O4WRR7WOPOEAT2/events.json","paper":"https://pith.science/paper/GI5PMAPZ"},"agent_actions":{"view_html":"https://pith.science/pith/GI5PMAPZNB25O4WRR7WOPOEAT2","download_json":"https://pith.science/pith/GI5PMAPZNB25O4WRR7WOPOEAT2.json","view_paper":"https://pith.science/paper/GI5PMAPZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.1825&json=true","fetch_graph":"https://pith.science/api/pith-number/GI5PMAPZNB25O4WRR7WOPOEAT2/graph.json","fetch_events":"https://pith.science/api/pith-number/GI5PMAPZNB25O4WRR7WOPOEAT2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GI5PMAPZNB25O4WRR7WOPOEAT2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GI5PMAPZNB25O4WRR7WOPOEAT2/action/storage_attestation","attest_author":"https://pith.science/pith/GI5PMAPZNB25O4WRR7WOPOEAT2/action/author_attestation","sign_citation":"https://pith.science/pith/GI5PMAPZNB25O4WRR7WOPOEAT2/action/citation_signature","submit_replication":"https://pith.science/pith/GI5PMAPZNB25O4WRR7WOPOEAT2/action/replication_record"}},"created_at":"2026-05-18T01:28:21.961095+00:00","updated_at":"2026-05-18T01:28:21.961095+00:00"}