{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:B362X5KMJRK6JKDX7PF67XBC2N","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":"c0797d845a5f8c0a6fe34c8358383882b8e9247a17d3aef154a057ca2219fdea","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-01-30T10:32:06Z","title_canon_sha256":"5ff3cb71b86375c740f5a733c1adf8890fc1e1c9db95c03856e382cb30ba5cb0"},"schema_version":"1.0","source":{"id":"0801.4636","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.4636","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"0801.4636v3","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.4636","created_at":"2026-05-18T04:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"B362X5KMJRK6","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"B362X5KMJRK6JKDX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"B362X5KM","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:07838bc7d56608219d22aaec39c016b191e04c25ab7c2e900dd4b5d9e23de3d8","target":"graph","created_at":"2026-05-18T04:25:13Z","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":"Let $K$ be a number field. Let $S$ be a finite set of places of $K$ containing all the archimedean ones. Let $R_S$ be the ring of $S$-integers of $K$. In the present paper we consider endomorphisms of $\\pro$ of degree 2, defined over $K$, with good reduction outside $S$. We prove that there exist only finitely many such endomorphisms, up to conjugation by ${\\rm PGL}_2(R_S)$, admitting a periodic point in $\\po$ of order $>3$. Also, all but finitely many classes with a periodic point in $\\po$ of order 3 are parametrized by an irreducible curve.","authors_text":"J.K. Canci","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-01-30T10:32:06Z","title":"Rational periodic points for quadratic maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.4636","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":"sha256:09d72eb2831e24df8d6ffdede7272915bb681bd5b4fe4ff2e5c5147bc423356f","target":"record","created_at":"2026-05-18T04:25:13Z","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":"c0797d845a5f8c0a6fe34c8358383882b8e9247a17d3aef154a057ca2219fdea","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-01-30T10:32:06Z","title_canon_sha256":"5ff3cb71b86375c740f5a733c1adf8890fc1e1c9db95c03856e382cb30ba5cb0"},"schema_version":"1.0","source":{"id":"0801.4636","kind":"arxiv","version":3}},"canonical_sha256":"0efdabf54c4c55e4a877fbcbefdc22d365cb1a5d04dfba5cc39c19187b8ddfd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0efdabf54c4c55e4a877fbcbefdc22d365cb1a5d04dfba5cc39c19187b8ddfd0","first_computed_at":"2026-05-18T04:25:13.481771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:13.481771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lYZ4B6ouBunxN7zMBfgCXjSrOqiZyHCzdfbeYt1BFJLQXH1Rltec0OkIL6juBCUMgk6wUwQHwsSPgLgrcUXdCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:13.482571Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.4636","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09d72eb2831e24df8d6ffdede7272915bb681bd5b4fe4ff2e5c5147bc423356f","sha256:07838bc7d56608219d22aaec39c016b191e04c25ab7c2e900dd4b5d9e23de3d8"],"state_sha256":"a69eef7c553cf6609d003af57f802f1bfc66f0c0e21a42aa878a9465b8ec67dd"}