{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CFQ6WXG5WM4XMEJYA2T7LK2B6B","short_pith_number":"pith:CFQ6WXG5","schema_version":"1.0","canonical_sha256":"1161eb5cddb33976113806a7f5ab41f050cb8ac71be30ac0bb4d845c7da8f45c","source":{"kind":"arxiv","id":"1404.3494","version":1},"attestation_state":"computed","paper":{"title":"Polynomial-Value Sieving and Recursively-Factorable Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jonathan Burns","submitted_at":"2014-04-14T08:55:07Z","abstract_excerpt":"We identify a recursive structure among factorizations of polynomial values into two integer factors. Polynomials for which this recursive structure characterizes all non-trivial representations of integer factorizations of the polynomial values into two parts are here called recursively-factorable polynomials. In particular, we prove that $n^2+1$ and the prime-producing polynomials $n^2+n+41$ and $2n^2+ 29$ are recursively-factorable.\n  For quadratics, the we prove that this recursive structure is equivalent to a Diophantine identity involving the product of two binary quadratic forms. We sho"},"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":"1404.3494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-14T08:55:07Z","cross_cats_sorted":[],"title_canon_sha256":"a749402f0340651c93cc845cccf7ea8a2a373360a24741dd5df12a355b4fa748","abstract_canon_sha256":"5d404092e94394f1b83f9ac1dc72ca787486292d5e2bf2854ae4d56f289c6654"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:15.100533Z","signature_b64":"UgH1olOyydkBJsJAxzk3G6KiGxkdbYFSlqg84sCFfjmV0jueRJYQ8QBJfa2X4BzgdgwO1EtrLWwYwVyhqPsxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1161eb5cddb33976113806a7f5ab41f050cb8ac71be30ac0bb4d845c7da8f45c","last_reissued_at":"2026-05-18T02:54:15.100103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:15.100103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomial-Value Sieving and Recursively-Factorable Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jonathan Burns","submitted_at":"2014-04-14T08:55:07Z","abstract_excerpt":"We identify a recursive structure among factorizations of polynomial values into two integer factors. Polynomials for which this recursive structure characterizes all non-trivial representations of integer factorizations of the polynomial values into two parts are here called recursively-factorable polynomials. In particular, we prove that $n^2+1$ and the prime-producing polynomials $n^2+n+41$ and $2n^2+ 29$ are recursively-factorable.\n  For quadratics, the we prove that this recursive structure is equivalent to a Diophantine identity involving the product of two binary quadratic forms. We sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3494","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":"1404.3494","created_at":"2026-05-18T02:54:15.100172+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.3494v1","created_at":"2026-05-18T02:54:15.100172+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3494","created_at":"2026-05-18T02:54:15.100172+00:00"},{"alias_kind":"pith_short_12","alias_value":"CFQ6WXG5WM4X","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CFQ6WXG5WM4XMEJY","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CFQ6WXG5","created_at":"2026-05-18T12:28:22.404517+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/CFQ6WXG5WM4XMEJYA2T7LK2B6B","json":"https://pith.science/pith/CFQ6WXG5WM4XMEJYA2T7LK2B6B.json","graph_json":"https://pith.science/api/pith-number/CFQ6WXG5WM4XMEJYA2T7LK2B6B/graph.json","events_json":"https://pith.science/api/pith-number/CFQ6WXG5WM4XMEJYA2T7LK2B6B/events.json","paper":"https://pith.science/paper/CFQ6WXG5"},"agent_actions":{"view_html":"https://pith.science/pith/CFQ6WXG5WM4XMEJYA2T7LK2B6B","download_json":"https://pith.science/pith/CFQ6WXG5WM4XMEJYA2T7LK2B6B.json","view_paper":"https://pith.science/paper/CFQ6WXG5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.3494&json=true","fetch_graph":"https://pith.science/api/pith-number/CFQ6WXG5WM4XMEJYA2T7LK2B6B/graph.json","fetch_events":"https://pith.science/api/pith-number/CFQ6WXG5WM4XMEJYA2T7LK2B6B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CFQ6WXG5WM4XMEJYA2T7LK2B6B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CFQ6WXG5WM4XMEJYA2T7LK2B6B/action/storage_attestation","attest_author":"https://pith.science/pith/CFQ6WXG5WM4XMEJYA2T7LK2B6B/action/author_attestation","sign_citation":"https://pith.science/pith/CFQ6WXG5WM4XMEJYA2T7LK2B6B/action/citation_signature","submit_replication":"https://pith.science/pith/CFQ6WXG5WM4XMEJYA2T7LK2B6B/action/replication_record"}},"created_at":"2026-05-18T02:54:15.100172+00:00","updated_at":"2026-05-18T02:54:15.100172+00:00"}