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Consequently, $$\\ln c_{j}>\\frac{1}{4}\\cdot2^{j}\\,\\,\\mathrm{for}\\,j\\geq5$$ If we also have $p\\equiv3\\,(\\mathrm{mod\\,4)}$ then $p^{2^{j-\\left\\lceil \\lg p\\right\\rceil }}$ divides $c_{j}$. Consequently, if $k\\geq3$, there exists some absolute constant $\\lambda>0$ so that, $$\\ln c_{j}>\\lambda k2^{j}\\mathrm{\\,\\,for\\,all\\,}j$$ These estimates argue against the possibility o"},"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":"1902.11164","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2019-02-27T18:55:33Z","cross_cats_sorted":[],"title_canon_sha256":"70817126e4c64eb070317216c682f5b31c534a9af0f956f6bc79b857f56342e5","abstract_canon_sha256":"a256c3b7a33b80282cc5c1dd222a96761e95c7db6657aa5f2dae25b99e36f501"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:25.602929Z","signature_b64":"U+Hl7ZSElTcgyVONlBF9zIn+ps9ApI2FsjBolNmBKE1fIlc3GZTXZb5rPN+ReLoaWjZFWmTuGUh44tg6YCCSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ab7d852b9a8cc414bd2456b1e556d306ffbdbacafef1fb6147a77b40dd7af95","last_reissued_at":"2026-05-17T23:52:25.602163Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:25.602163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coefficient growth in square chains","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shawn Walker","submitted_at":"2019-02-27T18:55:33Z","abstract_excerpt":"Suppose $((\\cdots((x^{2}-c_{1})^{2}-c_{2})^{2}\\cdots)^{2}-c_{k-1})^{2}-c_{k}$ splits into linear factors over $\\mathbb{Z}$ and $c_{k}\\neq0$. We show that for each $j$ and each prime $p$, if $p\\leq2^{j-1}$ then $p$ divides $c_{j}$. Consequently, $$\\ln c_{j}>\\frac{1}{4}\\cdot2^{j}\\,\\,\\mathrm{for}\\,j\\geq5$$ If we also have $p\\equiv3\\,(\\mathrm{mod\\,4)}$ then $p^{2^{j-\\left\\lceil \\lg p\\right\\rceil }}$ divides $c_{j}$. Consequently, if $k\\geq3$, there exists some absolute constant $\\lambda>0$ so that, $$\\ln c_{j}>\\lambda k2^{j}\\mathrm{\\,\\,for\\,all\\,}j$$ These estimates argue against the possibility o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.11164","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":"1902.11164","created_at":"2026-05-17T23:52:25.602302+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.11164v1","created_at":"2026-05-17T23:52:25.602302+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.11164","created_at":"2026-05-17T23:52:25.602302+00:00"},{"alias_kind":"pith_short_12","alias_value":"NK35QUVZVDGE","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"NK35QUVZVDGECS6S","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"NK35QUVZ","created_at":"2026-05-18T12:33:24.271573+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/NK35QUVZVDGECS6SIVVR4VLNGB","json":"https://pith.science/pith/NK35QUVZVDGECS6SIVVR4VLNGB.json","graph_json":"https://pith.science/api/pith-number/NK35QUVZVDGECS6SIVVR4VLNGB/graph.json","events_json":"https://pith.science/api/pith-number/NK35QUVZVDGECS6SIVVR4VLNGB/events.json","paper":"https://pith.science/paper/NK35QUVZ"},"agent_actions":{"view_html":"https://pith.science/pith/NK35QUVZVDGECS6SIVVR4VLNGB","download_json":"https://pith.science/pith/NK35QUVZVDGECS6SIVVR4VLNGB.json","view_paper":"https://pith.science/paper/NK35QUVZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.11164&json=true","fetch_graph":"https://pith.science/api/pith-number/NK35QUVZVDGECS6SIVVR4VLNGB/graph.json","fetch_events":"https://pith.science/api/pith-number/NK35QUVZVDGECS6SIVVR4VLNGB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NK35QUVZVDGECS6SIVVR4VLNGB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NK35QUVZVDGECS6SIVVR4VLNGB/action/storage_attestation","attest_author":"https://pith.science/pith/NK35QUVZVDGECS6SIVVR4VLNGB/action/author_attestation","sign_citation":"https://pith.science/pith/NK35QUVZVDGECS6SIVVR4VLNGB/action/citation_signature","submit_replication":"https://pith.science/pith/NK35QUVZVDGECS6SIVVR4VLNGB/action/replication_record"}},"created_at":"2026-05-17T23:52:25.602302+00:00","updated_at":"2026-05-17T23:52:25.602302+00:00"}