{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FDIYLDYSZOQOFMVAZGXKDUTIZ3","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":"244f9e5ba715808e45763a18f56db5b0c5e041b70a0803c9a59676934357405d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-02T15:48:31Z","title_canon_sha256":"68640b2483fffa5a8fff03ee36e04e55cd158fb49fd7eb1a451511653ecfc87d"},"schema_version":"1.0","source":{"id":"1509.00752","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00752","created_at":"2026-05-18T00:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00752v3","created_at":"2026-05-18T00:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00752","created_at":"2026-05-18T00:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"FDIYLDYSZOQO","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FDIYLDYSZOQOFMVA","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FDIYLDYS","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:58b7032ddd4e2c5fd7163f8724fec2603af1fee21ac0deae3201eeff65a061f1","target":"graph","created_at":"2026-05-18T00:33:24Z","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":"Over a number field $K$, a celebrated result of Silverman states that if $\\varphi(z)\\in K(z)$ is a rational function whose second iterate is not a polynomial, the set of $S$-integral points in the orbit $\\text{Orb}_\\varphi(P)=\\{\\varphi^n(P)\\}_{n\\geq0}$ is finite for all $P\\in \\mathbb{P}^1(K)$. In this paper, we show that if we vary $\\varphi$ and $P$ in a suitable family, the number of $S$-integral points in $\\text{Orb}_\\varphi(P)$ is absolutely bounded. In particular, if we fix $\\varphi$ and vary the basepoint $P\\in \\mathbb{P}^1(K)$, then we show that $\\#(\\text{Orb}_\\varphi(P)\\cap\\mathcal{O}_{","authors_text":"Wade Hindes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-02T15:48:31Z","title":"The average number of integral points in orbits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00752","kind":"arxiv","version":3},"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:e8bd81b43e5314e41454638e6b6387941145d0d4e563d185aa7e44e76fa4b6a3","target":"record","created_at":"2026-05-18T00:33:24Z","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":"244f9e5ba715808e45763a18f56db5b0c5e041b70a0803c9a59676934357405d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-02T15:48:31Z","title_canon_sha256":"68640b2483fffa5a8fff03ee36e04e55cd158fb49fd7eb1a451511653ecfc87d"},"schema_version":"1.0","source":{"id":"1509.00752","kind":"arxiv","version":3}},"canonical_sha256":"28d1858f12cba0e2b2a0c9aea1d268cefa8c219075e112d611dbf192d8c8a48f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28d1858f12cba0e2b2a0c9aea1d268cefa8c219075e112d611dbf192d8c8a48f","first_computed_at":"2026-05-18T00:33:24.143915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:24.143915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dIAg/6VTz1PqI3lU62gF4hWdnSB8gYgVTA0M8LN1uedIsluuY9UY+MqOarIYY1UaMXivYlNJUeuJeMSUgK8MDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:24.144731Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00752","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8bd81b43e5314e41454638e6b6387941145d0d4e563d185aa7e44e76fa4b6a3","sha256:58b7032ddd4e2c5fd7163f8724fec2603af1fee21ac0deae3201eeff65a061f1"],"state_sha256":"9e524f8d0d9c820b9fb870401378bc831a2ac6028052bf7e6ffc81e98371f598"}