{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:U3JQK34TOWSIY5IBDHEDYSDFFS","short_pith_number":"pith:U3JQK34T","schema_version":"1.0","canonical_sha256":"a6d3056f9375a48c750119c83c48652c9757dffd6bf1db781d0fe21ba405c8f3","source":{"kind":"arxiv","id":"1710.04332","version":1},"attestation_state":"computed","paper":{"title":"Riccati equations and polynomial dynamics over function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rafe Jones, Wade Hindes","submitted_at":"2017-10-12T00:22:21Z","abstract_excerpt":"Given a function field $K$ and $\\phi \\in K[x]$, we study two finiteness questions related to iteration of $\\phi$: whether all but finitely many terms of an orbit of $\\phi$ must possess a primitive prime divisor, and whether the Galois groups of iterates of $\\phi$ must have finite index in their natural overgroup $\\text{Aut}(T_d)$, where $T_d$ is the infinite tree of iterated preimages of $0$ under $\\phi$. We focus particularly on the case where $K$ has characteristic $p$, where far less is known. We resolve the first question in the affirmative under relatively weak hypotheses; interestingly, "},"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":"1710.04332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-12T00:22:21Z","cross_cats_sorted":[],"title_canon_sha256":"49620fc4454199627287718d1f6a053f04a167bab4926945b14422655b081f6c","abstract_canon_sha256":"00768183d7e6e0b48124b8d0f6a341c054816b8f8403dd06b84ebc71e17e0bd7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:01.360301Z","signature_b64":"MHZWtHSWHp0F3nGEdXdU2mi2RnjNkjfv7u8nieLzc3+4HP9JsKyIc2Z+nKg+2y+4IWrO1IgUciZq/c2lxk/XAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6d3056f9375a48c750119c83c48652c9757dffd6bf1db781d0fe21ba405c8f3","last_reissued_at":"2026-05-18T00:33:01.359728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:01.359728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Riccati equations and polynomial dynamics over function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rafe Jones, Wade Hindes","submitted_at":"2017-10-12T00:22:21Z","abstract_excerpt":"Given a function field $K$ and $\\phi \\in K[x]$, we study two finiteness questions related to iteration of $\\phi$: whether all but finitely many terms of an orbit of $\\phi$ must possess a primitive prime divisor, and whether the Galois groups of iterates of $\\phi$ must have finite index in their natural overgroup $\\text{Aut}(T_d)$, where $T_d$ is the infinite tree of iterated preimages of $0$ under $\\phi$. We focus particularly on the case where $K$ has characteristic $p$, where far less is known. We resolve the first question in the affirmative under relatively weak hypotheses; interestingly, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04332","kind":"arxiv","version":1},"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":"1710.04332","created_at":"2026-05-18T00:33:01.359839+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.04332v1","created_at":"2026-05-18T00:33:01.359839+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04332","created_at":"2026-05-18T00:33:01.359839+00:00"},{"alias_kind":"pith_short_12","alias_value":"U3JQK34TOWSI","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"U3JQK34TOWSIY5IB","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"U3JQK34T","created_at":"2026-05-18T12:31:46.661854+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/U3JQK34TOWSIY5IBDHEDYSDFFS","json":"https://pith.science/pith/U3JQK34TOWSIY5IBDHEDYSDFFS.json","graph_json":"https://pith.science/api/pith-number/U3JQK34TOWSIY5IBDHEDYSDFFS/graph.json","events_json":"https://pith.science/api/pith-number/U3JQK34TOWSIY5IBDHEDYSDFFS/events.json","paper":"https://pith.science/paper/U3JQK34T"},"agent_actions":{"view_html":"https://pith.science/pith/U3JQK34TOWSIY5IBDHEDYSDFFS","download_json":"https://pith.science/pith/U3JQK34TOWSIY5IBDHEDYSDFFS.json","view_paper":"https://pith.science/paper/U3JQK34T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.04332&json=true","fetch_graph":"https://pith.science/api/pith-number/U3JQK34TOWSIY5IBDHEDYSDFFS/graph.json","fetch_events":"https://pith.science/api/pith-number/U3JQK34TOWSIY5IBDHEDYSDFFS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U3JQK34TOWSIY5IBDHEDYSDFFS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U3JQK34TOWSIY5IBDHEDYSDFFS/action/storage_attestation","attest_author":"https://pith.science/pith/U3JQK34TOWSIY5IBDHEDYSDFFS/action/author_attestation","sign_citation":"https://pith.science/pith/U3JQK34TOWSIY5IBDHEDYSDFFS/action/citation_signature","submit_replication":"https://pith.science/pith/U3JQK34TOWSIY5IBDHEDYSDFFS/action/replication_record"}},"created_at":"2026-05-18T00:33:01.359839+00:00","updated_at":"2026-05-18T00:33:01.359839+00:00"}