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We prove that the set of (m,n) in N^2 such that f^m(u) is S-integral relative to f^n(w) is finite and effectively computable. This may be thought of as a two-parameter analog of a result of Silverman on integral points in orbits of rational maps.\n  This issue can be translated in terms of integral points on an open subset of P_1^2; then one can apply a modern version of the method of Runge, after i"},"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":"1201.1313","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-01-05T21:57:46Z","cross_cats_sorted":[],"title_canon_sha256":"2d8ef6ec30ffdc44d85961173fd7318504bf5e74dc25de7e7f000679a6304bb9","abstract_canon_sha256":"93bc38e1aee82e5d1157b157d0f347bee41ede1e1ab435d55091de76b5441cef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:37.645873Z","signature_b64":"lbiTHE1PMmlD+QseZtyB2oul9YKEhAzh7JxKtFQchO5WFQn/WTj6vce5XF72SHcpMxQ/nwgy0h9co1nqbVaIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9517cc5e2509655d3327351a05736170749f4d2c7ad169d783dd859565c01b04","last_reissued_at":"2026-05-18T04:00:37.645222Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:37.645222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integral points in two-parameter orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pietro Corvaja, Thomas J. Tucker, Umberto Zannier, Vijay Sookdeo","submitted_at":"2012-01-05T21:57:46Z","abstract_excerpt":"Let K be a number field, let f: P_1 --> P_1 be a nonconstant rational map of degree greater than 1, let S be a finite set of places of K, and suppose that u, w in P_1(K) are not preperiodic under f. We prove that the set of (m,n) in N^2 such that f^m(u) is S-integral relative to f^n(w) is finite and effectively computable. This may be thought of as a two-parameter analog of a result of Silverman on integral points in orbits of rational maps.\n  This issue can be translated in terms of integral points on an open subset of P_1^2; then one can apply a modern version of the method of Runge, after i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1313","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":"1201.1313","created_at":"2026-05-18T04:00:37.645341+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.1313v2","created_at":"2026-05-18T04:00:37.645341+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1313","created_at":"2026-05-18T04:00:37.645341+00:00"},{"alias_kind":"pith_short_12","alias_value":"SUL4YXRFBFSV","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"SUL4YXRFBFSV2MZH","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"SUL4YXRF","created_at":"2026-05-18T12:27:23.164592+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/SUL4YXRFBFSV2MZHGUNAK43BOB","json":"https://pith.science/pith/SUL4YXRFBFSV2MZHGUNAK43BOB.json","graph_json":"https://pith.science/api/pith-number/SUL4YXRFBFSV2MZHGUNAK43BOB/graph.json","events_json":"https://pith.science/api/pith-number/SUL4YXRFBFSV2MZHGUNAK43BOB/events.json","paper":"https://pith.science/paper/SUL4YXRF"},"agent_actions":{"view_html":"https://pith.science/pith/SUL4YXRFBFSV2MZHGUNAK43BOB","download_json":"https://pith.science/pith/SUL4YXRFBFSV2MZHGUNAK43BOB.json","view_paper":"https://pith.science/paper/SUL4YXRF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.1313&json=true","fetch_graph":"https://pith.science/api/pith-number/SUL4YXRFBFSV2MZHGUNAK43BOB/graph.json","fetch_events":"https://pith.science/api/pith-number/SUL4YXRFBFSV2MZHGUNAK43BOB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SUL4YXRFBFSV2MZHGUNAK43BOB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SUL4YXRFBFSV2MZHGUNAK43BOB/action/storage_attestation","attest_author":"https://pith.science/pith/SUL4YXRFBFSV2MZHGUNAK43BOB/action/author_attestation","sign_citation":"https://pith.science/pith/SUL4YXRFBFSV2MZHGUNAK43BOB/action/citation_signature","submit_replication":"https://pith.science/pith/SUL4YXRFBFSV2MZHGUNAK43BOB/action/replication_record"}},"created_at":"2026-05-18T04:00:37.645341+00:00","updated_at":"2026-05-18T04:00:37.645341+00:00"}