{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FEBCIFSFK5CRKUIW2YOVTXNQHP","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":"da41353e84bad6285b587181ce832b4d92ca525443ebad8a16447881c2838400","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-15T18:01:20Z","title_canon_sha256":"4355b7547a34d64c6ed7bb63a98a8c15ab9e86b861b6c0c39eddc3dda829c9bd"},"schema_version":"1.0","source":{"id":"1210.4127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4127","created_at":"2026-05-18T01:22:26Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4127v1","created_at":"2026-05-18T01:22:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4127","created_at":"2026-05-18T01:22:26Z"},{"alias_kind":"pith_short_12","alias_value":"FEBCIFSFK5CR","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FEBCIFSFK5CRKUIW","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FEBCIFSF","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:3c1f6efdd2ffc0e16b562cbbb037ee2fe35f83e2590d5980b7c012644485a3af","target":"graph","created_at":"2026-05-18T01:22:26Z","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":"We examine the question of when a quadratic polynomial f(x) defined over a number field K can have a newly reducible nth iterate, that is, f^n(x) irreducible over K but f^{n+1}(x) reducible over K, where f^n denotes the nth iterate of f. For each choice of critical point \\gamma of f(x), we consider the family\ng_{\\gamma,m}(x)= (x - \\gamma)^2 + m + \\gamma, m \\in K.\nFor fixed n \\geq 3 and nearly all values of \\gamma, we show that there are only finitely many m such that g_{\\gamma,m} has a newly reducible nth iterate. For n = 2 we show a similar result for a much more restricted set of \\gamma. The","authors_text":"Emma Colbert, Katharine Chamberlin, Patrick Hefferman, Rafe Jones, Sarah Orchard, Sharon Frechette","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-15T18:01:20Z","title":"Newly reducible iterates in families of quadratic polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4127","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":"sha256:9392b40b055db144ff6b7f089e09be471c398ab1c38e81fe487aa12620d98bd7","target":"record","created_at":"2026-05-18T01:22:26Z","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":"da41353e84bad6285b587181ce832b4d92ca525443ebad8a16447881c2838400","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-15T18:01:20Z","title_canon_sha256":"4355b7547a34d64c6ed7bb63a98a8c15ab9e86b861b6c0c39eddc3dda829c9bd"},"schema_version":"1.0","source":{"id":"1210.4127","kind":"arxiv","version":1}},"canonical_sha256":"29022416455745155116d61d59ddb03bc0d54f0af9b9a3e7df5284bd5fc3c0d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29022416455745155116d61d59ddb03bc0d54f0af9b9a3e7df5284bd5fc3c0d8","first_computed_at":"2026-05-18T01:22:26.160175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:26.160175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"96H0IWXsMA37nd1511AqmtQdcEi1NKQbIoxOb05u6PVWbTP5+PIkjPkn+nkuyIyrD0jgjr/kcV8FrhuOaNN4BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:26.160860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9392b40b055db144ff6b7f089e09be471c398ab1c38e81fe487aa12620d98bd7","sha256:3c1f6efdd2ffc0e16b562cbbb037ee2fe35f83e2590d5980b7c012644485a3af"],"state_sha256":"035057e3e73aee93bb1fec9dcc44173172df37744baa1461e20a18ee8f5a59e4"}