{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BT2OGI3XDKUO4ZXAXASMBWCQ4P","short_pith_number":"pith:BT2OGI3X","schema_version":"1.0","canonical_sha256":"0cf4e323771aa8ee66e0b824c0d850e3d430d2721997a7e3cbe112f75ed9aff5","source":{"kind":"arxiv","id":"1511.06081","version":2},"attestation_state":"computed","paper":{"title":"The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for split rational maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DS"],"primary_cat":"math.NT","authors_text":"Dragos Ghioca, Hexi Ye, Khoa D. Nguyen","submitted_at":"2015-11-19T07:31:49Z","abstract_excerpt":"We prove the Dynamical Bogomolov Conjecture for endomorphisms of P^1\\times P^1 defined over a number field. We use the equidistribution theorem for points of small height with respect to an algebraic dynamical system, combined with a theorem of Levin regarding symmetries of the Julia set. Using a specialization theorem of Yuan and Zhang, we prove the Dynamical Manin-Mumford Conjecture for endomorhisms of P^1\\times P^1 defined over the complex numbers."},"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":"1511.06081","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-19T07:31:49Z","cross_cats_sorted":["math.AG","math.DS"],"title_canon_sha256":"5c8cb4eb87cc2f7348590d7f012dcf7d423659ebe82e0a9c81af261d5f775c55","abstract_canon_sha256":"1d63b651d78cf1ac5324afa6adba6448980dd61f0f64b4cb9eaf29d06c9504cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:05.789516Z","signature_b64":"ykh4o6Gmwe1XL2Dh+d6Ds2EzQbfdNCxUwDhJLIJxIgOQz5y4Bq6eXg/BuSTPiMJxfCuHK8pQYSSDerbyLWffDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cf4e323771aa8ee66e0b824c0d850e3d430d2721997a7e3cbe112f75ed9aff5","last_reissued_at":"2026-05-18T01:04:05.789026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:05.789026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for split rational maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DS"],"primary_cat":"math.NT","authors_text":"Dragos Ghioca, Hexi Ye, Khoa D. Nguyen","submitted_at":"2015-11-19T07:31:49Z","abstract_excerpt":"We prove the Dynamical Bogomolov Conjecture for endomorphisms of P^1\\times P^1 defined over a number field. We use the equidistribution theorem for points of small height with respect to an algebraic dynamical system, combined with a theorem of Levin regarding symmetries of the Julia set. Using a specialization theorem of Yuan and Zhang, we prove the Dynamical Manin-Mumford Conjecture for endomorhisms of P^1\\times P^1 defined over the complex numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06081","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":"1511.06081","created_at":"2026-05-18T01:04:05.789106+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.06081v2","created_at":"2026-05-18T01:04:05.789106+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06081","created_at":"2026-05-18T01:04:05.789106+00:00"},{"alias_kind":"pith_short_12","alias_value":"BT2OGI3XDKUO","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BT2OGI3XDKUO4ZXA","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BT2OGI3X","created_at":"2026-05-18T12:29:14.074870+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/BT2OGI3XDKUO4ZXAXASMBWCQ4P","json":"https://pith.science/pith/BT2OGI3XDKUO4ZXAXASMBWCQ4P.json","graph_json":"https://pith.science/api/pith-number/BT2OGI3XDKUO4ZXAXASMBWCQ4P/graph.json","events_json":"https://pith.science/api/pith-number/BT2OGI3XDKUO4ZXAXASMBWCQ4P/events.json","paper":"https://pith.science/paper/BT2OGI3X"},"agent_actions":{"view_html":"https://pith.science/pith/BT2OGI3XDKUO4ZXAXASMBWCQ4P","download_json":"https://pith.science/pith/BT2OGI3XDKUO4ZXAXASMBWCQ4P.json","view_paper":"https://pith.science/paper/BT2OGI3X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.06081&json=true","fetch_graph":"https://pith.science/api/pith-number/BT2OGI3XDKUO4ZXAXASMBWCQ4P/graph.json","fetch_events":"https://pith.science/api/pith-number/BT2OGI3XDKUO4ZXAXASMBWCQ4P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BT2OGI3XDKUO4ZXAXASMBWCQ4P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BT2OGI3XDKUO4ZXAXASMBWCQ4P/action/storage_attestation","attest_author":"https://pith.science/pith/BT2OGI3XDKUO4ZXAXASMBWCQ4P/action/author_attestation","sign_citation":"https://pith.science/pith/BT2OGI3XDKUO4ZXAXASMBWCQ4P/action/citation_signature","submit_replication":"https://pith.science/pith/BT2OGI3XDKUO4ZXAXASMBWCQ4P/action/replication_record"}},"created_at":"2026-05-18T01:04:05.789106+00:00","updated_at":"2026-05-18T01:04:05.789106+00:00"}