{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:U3JQK34TOWSIY5IBDHEDYSDFFS","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":"00768183d7e6e0b48124b8d0f6a341c054816b8f8403dd06b84ebc71e17e0bd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-12T00:22:21Z","title_canon_sha256":"49620fc4454199627287718d1f6a053f04a167bab4926945b14422655b081f6c"},"schema_version":"1.0","source":{"id":"1710.04332","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.04332","created_at":"2026-05-18T00:33:01Z"},{"alias_kind":"arxiv_version","alias_value":"1710.04332v1","created_at":"2026-05-18T00:33:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04332","created_at":"2026-05-18T00:33:01Z"},{"alias_kind":"pith_short_12","alias_value":"U3JQK34TOWSI","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"U3JQK34TOWSIY5IB","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"U3JQK34T","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:3962aa5b6c4f9bac312ad94dd607dec2147dbce4f1d5daffb2097303e6b95f91","target":"graph","created_at":"2026-05-18T00:33:01Z","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":"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, ","authors_text":"Rafe Jones, Wade Hindes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-12T00:22:21Z","title":"Riccati equations and polynomial dynamics over function fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04332","kind":"arxiv","version":1},"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":"sha256:01f6ab86202f84d3cf489605f65e44d7811fa23f2187c9d2fdb60039d5a64cc7","target":"record","created_at":"2026-05-18T00:33:01Z","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":"00768183d7e6e0b48124b8d0f6a341c054816b8f8403dd06b84ebc71e17e0bd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-12T00:22:21Z","title_canon_sha256":"49620fc4454199627287718d1f6a053f04a167bab4926945b14422655b081f6c"},"schema_version":"1.0","source":{"id":"1710.04332","kind":"arxiv","version":1}},"canonical_sha256":"a6d3056f9375a48c750119c83c48652c9757dffd6bf1db781d0fe21ba405c8f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6d3056f9375a48c750119c83c48652c9757dffd6bf1db781d0fe21ba405c8f3","first_computed_at":"2026-05-18T00:33:01.359728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:01.359728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MHZWtHSWHp0F3nGEdXdU2mi2RnjNkjfv7u8nieLzc3+4HP9JsKyIc2Z+nKg+2y+4IWrO1IgUciZq/c2lxk/XAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:01.360301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.04332","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01f6ab86202f84d3cf489605f65e44d7811fa23f2187c9d2fdb60039d5a64cc7","sha256:3962aa5b6c4f9bac312ad94dd607dec2147dbce4f1d5daffb2097303e6b95f91"],"state_sha256":"e7e1b4c6f88ded6989eed86620d10c1d54304773129d67e081a2c5fd851414d3"}