{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:7IK4BJ6QRIL566KRD4BK7B77VS","short_pith_number":"pith:7IK4BJ6Q","schema_version":"1.0","canonical_sha256":"fa15c0a7d08a17df79511f02af87ffaca44e496304704d5eaa3ea4124a888e4b","source":{"kind":"arxiv","id":"1704.02204","version":1},"attestation_state":"computed","paper":{"title":"The set of stable primes for polynomial sequences with large Galois group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrea Ferraguti","submitted_at":"2017-04-07T12:26:55Z","abstract_excerpt":"Let $K$ be a number field with ring of integers $\\mathcal O_K$, and let $\\{f_k\\}_{k\\in \\mathbb N}\\subseteq \\mathcal O_K[x]$ be a sequence of monic polynomials such that for every $n\\in \\mathbb N$, the composition $f^{(n)}=f_1\\circ f_2\\circ\\ldots\\circ f_n$ is irreducible. In this paper we show that if the size of the Galois group of $f^{(n)}$ is large enough (in a precise sense) as a function of $n$, then the set of primes $\\mathfrak p\\subseteq\\mathcal O_K$ such that every $f^{(n)}$ is irreducible modulo $\\mathfrak p$ has density zero. Moreover, we prove that the subset of polynomial sequences "},"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":"1704.02204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-07T12:26:55Z","cross_cats_sorted":[],"title_canon_sha256":"9090bcd908a6c33396c8dba7b02d777bb9439f2a90b77ab2b7c59a7ab689cc85","abstract_canon_sha256":"4a5f31ca577e7f258c9eb45101011355f5ff1247c1aed7101e99feffaab7aa5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:50.427656Z","signature_b64":"GRe7ZGdYSybbYR43AnPBuhnOf1ix0R8wZ8MsYZ6lELIQ+uwbQuJgApHuolip0DD0pZd3v0wzjMJ1a3FPlvt5DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa15c0a7d08a17df79511f02af87ffaca44e496304704d5eaa3ea4124a888e4b","last_reissued_at":"2026-05-18T00:46:50.427103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:50.427103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The set of stable primes for polynomial sequences with large Galois group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrea Ferraguti","submitted_at":"2017-04-07T12:26:55Z","abstract_excerpt":"Let $K$ be a number field with ring of integers $\\mathcal O_K$, and let $\\{f_k\\}_{k\\in \\mathbb N}\\subseteq \\mathcal O_K[x]$ be a sequence of monic polynomials such that for every $n\\in \\mathbb N$, the composition $f^{(n)}=f_1\\circ f_2\\circ\\ldots\\circ f_n$ is irreducible. In this paper we show that if the size of the Galois group of $f^{(n)}$ is large enough (in a precise sense) as a function of $n$, then the set of primes $\\mathfrak p\\subseteq\\mathcal O_K$ such that every $f^{(n)}$ is irreducible modulo $\\mathfrak p$ has density zero. Moreover, we prove that the subset of polynomial sequences "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02204","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":"1704.02204","created_at":"2026-05-18T00:46:50.427194+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.02204v1","created_at":"2026-05-18T00:46:50.427194+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02204","created_at":"2026-05-18T00:46:50.427194+00:00"},{"alias_kind":"pith_short_12","alias_value":"7IK4BJ6QRIL5","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"7IK4BJ6QRIL566KR","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"7IK4BJ6Q","created_at":"2026-05-18T12:31:05.417338+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/7IK4BJ6QRIL566KRD4BK7B77VS","json":"https://pith.science/pith/7IK4BJ6QRIL566KRD4BK7B77VS.json","graph_json":"https://pith.science/api/pith-number/7IK4BJ6QRIL566KRD4BK7B77VS/graph.json","events_json":"https://pith.science/api/pith-number/7IK4BJ6QRIL566KRD4BK7B77VS/events.json","paper":"https://pith.science/paper/7IK4BJ6Q"},"agent_actions":{"view_html":"https://pith.science/pith/7IK4BJ6QRIL566KRD4BK7B77VS","download_json":"https://pith.science/pith/7IK4BJ6QRIL566KRD4BK7B77VS.json","view_paper":"https://pith.science/paper/7IK4BJ6Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.02204&json=true","fetch_graph":"https://pith.science/api/pith-number/7IK4BJ6QRIL566KRD4BK7B77VS/graph.json","fetch_events":"https://pith.science/api/pith-number/7IK4BJ6QRIL566KRD4BK7B77VS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7IK4BJ6QRIL566KRD4BK7B77VS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7IK4BJ6QRIL566KRD4BK7B77VS/action/storage_attestation","attest_author":"https://pith.science/pith/7IK4BJ6QRIL566KRD4BK7B77VS/action/author_attestation","sign_citation":"https://pith.science/pith/7IK4BJ6QRIL566KRD4BK7B77VS/action/citation_signature","submit_replication":"https://pith.science/pith/7IK4BJ6QRIL566KRD4BK7B77VS/action/replication_record"}},"created_at":"2026-05-18T00:46:50.427194+00:00","updated_at":"2026-05-18T00:46:50.427194+00:00"}