{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:J364ZQR2VEOEHOEISVGKO4DHD4","short_pith_number":"pith:J364ZQR2","schema_version":"1.0","canonical_sha256":"4efdccc23aa91c43b888954ca770671f35f03a58c5ab7c59e0b81687e5ec96d0","source":{"kind":"arxiv","id":"1312.6767","version":2},"attestation_state":"computed","paper":{"title":"A Refined Conjecture For Factoring Iterates Of Quadratic Polynomials Over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nigel Boston, Shixiang Xia, Vefa Goksel","submitted_at":"2013-12-24T07:08:36Z","abstract_excerpt":"Jones and Boston conjectured that the factorization process for iterates of irreducible quadratic polynomials over finite fields is approximated by a Markov model. In this paper, we find unexpected and intricate behavior for some quadratic polynomials, in particular for the ones with tail size one. We also propose a multi-step Markov model that explains these new observations better than the model of Jones and Boston."},"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":"1312.6767","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-24T07:08:36Z","cross_cats_sorted":[],"title_canon_sha256":"e908933ae69ac0faeab633fa9b4050854af7371d11f0a966eaad47df26fdbe27","abstract_canon_sha256":"61b70e3e741c4f5ca4b23bcdebd53eeea81163cb1c7b84ad091df410561c18b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:46.573346Z","signature_b64":"rD+3bvFxbqp7gK4EGwzj8P7ckYHEBHmL7q6ig9o0IhJveek7KwuI/JkxI8GZF6t3viCCkf8IaWgQ5KbVs5eTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4efdccc23aa91c43b888954ca770671f35f03a58c5ab7c59e0b81687e5ec96d0","last_reissued_at":"2026-05-18T03:03:46.572601Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:46.572601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Refined Conjecture For Factoring Iterates Of Quadratic Polynomials Over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nigel Boston, Shixiang Xia, Vefa Goksel","submitted_at":"2013-12-24T07:08:36Z","abstract_excerpt":"Jones and Boston conjectured that the factorization process for iterates of irreducible quadratic polynomials over finite fields is approximated by a Markov model. In this paper, we find unexpected and intricate behavior for some quadratic polynomials, in particular for the ones with tail size one. We also propose a multi-step Markov model that explains these new observations better than the model of Jones and Boston."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6767","kind":"arxiv","version":2},"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":"1312.6767","created_at":"2026-05-18T03:03:46.572726+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.6767v2","created_at":"2026-05-18T03:03:46.572726+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6767","created_at":"2026-05-18T03:03:46.572726+00:00"},{"alias_kind":"pith_short_12","alias_value":"J364ZQR2VEOE","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"J364ZQR2VEOEHOEI","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"J364ZQR2","created_at":"2026-05-18T12:27:49.015174+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/J364ZQR2VEOEHOEISVGKO4DHD4","json":"https://pith.science/pith/J364ZQR2VEOEHOEISVGKO4DHD4.json","graph_json":"https://pith.science/api/pith-number/J364ZQR2VEOEHOEISVGKO4DHD4/graph.json","events_json":"https://pith.science/api/pith-number/J364ZQR2VEOEHOEISVGKO4DHD4/events.json","paper":"https://pith.science/paper/J364ZQR2"},"agent_actions":{"view_html":"https://pith.science/pith/J364ZQR2VEOEHOEISVGKO4DHD4","download_json":"https://pith.science/pith/J364ZQR2VEOEHOEISVGKO4DHD4.json","view_paper":"https://pith.science/paper/J364ZQR2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.6767&json=true","fetch_graph":"https://pith.science/api/pith-number/J364ZQR2VEOEHOEISVGKO4DHD4/graph.json","fetch_events":"https://pith.science/api/pith-number/J364ZQR2VEOEHOEISVGKO4DHD4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J364ZQR2VEOEHOEISVGKO4DHD4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J364ZQR2VEOEHOEISVGKO4DHD4/action/storage_attestation","attest_author":"https://pith.science/pith/J364ZQR2VEOEHOEISVGKO4DHD4/action/author_attestation","sign_citation":"https://pith.science/pith/J364ZQR2VEOEHOEISVGKO4DHD4/action/citation_signature","submit_replication":"https://pith.science/pith/J364ZQR2VEOEHOEISVGKO4DHD4/action/replication_record"}},"created_at":"2026-05-18T03:03:46.572726+00:00","updated_at":"2026-05-18T03:03:46.572726+00:00"}