{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GI5PMAPZNB25O4WRR7WOPOEAT2","short_pith_number":"pith:GI5PMAPZ","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"},"canonical_sha256":"323af601f96875d772d18fece7b8809eb7709c544e7c8bf5d12ec0e91fed77c8","source":{"kind":"arxiv","id":"1106.1825","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1825","created_at":"2026-05-18T01:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1825v2","created_at":"2026-05-18T01:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1825","created_at":"2026-05-18T01:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"GI5PMAPZNB25","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GI5PMAPZNB25O4WR","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GI5PMAPZ","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GI5PMAPZNB25O4WRR7WOPOEAT2","target":"record","payload":{"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"},"canonical_sha256":"323af601f96875d772d18fece7b8809eb7709c544e7c8bf5d12ec0e91fed77c8","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"},"source_kind":"arxiv","source_id":"1106.1825","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:28:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yWnIrkJxWI8iLGvhE/4e2ZvNBnEy8degP4imPTYkRoEKsB+jd760/hmgs9ZxaV1m4hP9qhLLkHkrT61330q7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:34:40.663602Z"},"content_sha256":"442cd3be1705afccf265c0aa19c20c6f6a2d86967fc07f5fabb36a5aaf5be2c5","schema_version":"1.0","event_id":"sha256:442cd3be1705afccf265c0aa19c20c6f6a2d86967fc07f5fabb36a5aaf5be2c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GI5PMAPZNB25O4WRR7WOPOEAT2","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:28:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OXH+tMMX4U4gbFq0AWlYL9U8oepxX8gMtm5xsr+IBeXyTtJFYpBo8JQeH+BdaMiB8PtmIKNgEUi0iP9FeP3cCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:34:40.663934Z"},"content_sha256":"c6b4b59da3ab220d8f2a8ab6b4ccd31c52f90d8ff93e8d6902946486a6c93867","schema_version":"1.0","event_id":"sha256:c6b4b59da3ab220d8f2a8ab6b4ccd31c52f90d8ff93e8d6902946486a6c93867"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GI5PMAPZNB25O4WRR7WOPOEAT2/bundle.json","state_url":"https://pith.science/pith/GI5PMAPZNB25O4WRR7WOPOEAT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GI5PMAPZNB25O4WRR7WOPOEAT2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T03:34:40Z","links":{"resolver":"https://pith.science/pith/GI5PMAPZNB25O4WRR7WOPOEAT2","bundle":"https://pith.science/pith/GI5PMAPZNB25O4WRR7WOPOEAT2/bundle.json","state":"https://pith.science/pith/GI5PMAPZNB25O4WRR7WOPOEAT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GI5PMAPZNB25O4WRR7WOPOEAT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GI5PMAPZNB25O4WRR7WOPOEAT2","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":"cba1b2390709a358dfe6e73bd57e4a297a75d4cbf715563048d54388d6fe6b8e","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-09T14:06:47Z","title_canon_sha256":"d288d297ac538649e88a0036af08b3ef09c3dc14f950369884d50e422b6d9c4b"},"schema_version":"1.0","source":{"id":"1106.1825","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1825","created_at":"2026-05-18T01:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1825v2","created_at":"2026-05-18T01:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1825","created_at":"2026-05-18T01:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"GI5PMAPZNB25","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GI5PMAPZNB25O4WR","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GI5PMAPZ","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:c6b4b59da3ab220d8f2a8ab6b4ccd31c52f90d8ff93e8d6902946486a6c93867","target":"graph","created_at":"2026-05-18T01:28:21Z","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 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.","authors_text":"Junyi Xie","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-09T14:06:47Z","title":"Periodic points of birational maps on projective surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1825","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":"sha256:442cd3be1705afccf265c0aa19c20c6f6a2d86967fc07f5fabb36a5aaf5be2c5","target":"record","created_at":"2026-05-18T01:28:21Z","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":"cba1b2390709a358dfe6e73bd57e4a297a75d4cbf715563048d54388d6fe6b8e","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-09T14:06:47Z","title_canon_sha256":"d288d297ac538649e88a0036af08b3ef09c3dc14f950369884d50e422b6d9c4b"},"schema_version":"1.0","source":{"id":"1106.1825","kind":"arxiv","version":2}},"canonical_sha256":"323af601f96875d772d18fece7b8809eb7709c544e7c8bf5d12ec0e91fed77c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"323af601f96875d772d18fece7b8809eb7709c544e7c8bf5d12ec0e91fed77c8","first_computed_at":"2026-05-18T01:28:21.961011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:21.961011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UWA8RMVWxI+562k1zZjOpvI8NipKhH257pL0TQ99fivA4gikeP4AL2lFeNgK3IE/bgoZDKKoNTxLuO4fTS4WBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:21.961652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1825","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:442cd3be1705afccf265c0aa19c20c6f6a2d86967fc07f5fabb36a5aaf5be2c5","sha256:c6b4b59da3ab220d8f2a8ab6b4ccd31c52f90d8ff93e8d6902946486a6c93867"],"state_sha256":"3460468fa2a50acdb40de1b49c03e588a7cbc50e16b26f1e2f5bd8716e152524"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U8Lpf5WFauIiqPEAY18q/01Oj0Mu8DH8WrkgMQeAUy7CFSLOEtkl5H7/ChbwN2gSIpZNprcQSKUvgOOIpfHCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T03:34:40.665831Z","bundle_sha256":"dbd006f7e23ff17f2d68d04b9127e331fe9b1f55419ce8dd026217cbe2539a27"}}