{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:3S343FNHSVAKJDRKST5RLLRSOT","short_pith_number":"pith:3S343FNH","schema_version":"1.0","canonical_sha256":"dcb7cd95a79540a48e2a94fb15ae3274e3981f25cc339469699b406322f97aca","source":{"kind":"arxiv","id":"0809.4381","version":2},"attestation_state":"computed","paper":{"title":"Representing an element in F_q[t] as the sum of two irreducibles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andreas O. Bender","submitted_at":"2008-09-25T11:33:52Z","abstract_excerpt":"A monic polynomial in F_q[t] of degree n over a finite field F_q of odd characteristic can be written as the sum of two irreducible monic elements in F_q[t] of degrees n and n-1 if q is larger than a bound depending only on n. The main tool is a sufficient condition for simultaneous primality of two polynomials in one variable x with coefficients in F_q[t]."},"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":"0809.4381","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-09-25T11:33:52Z","cross_cats_sorted":[],"title_canon_sha256":"a50d812f60bdb116211361d46ec5515f61a66673352ea77dd9118d2ab041b8ca","abstract_canon_sha256":"ae1fe87bc0e17d9e55919fd6d81f52b04ce74e8bab74692080dac1710db16d49"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:44.816826Z","signature_b64":"4p6h3Q1Yt5KxX6WQaN7fi0ByxfMykfiLMhhP/6IbsJbkSgyQF7GDJYRgGieyLijxjSCk+tHxIwfpJKopBSDnDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcb7cd95a79540a48e2a94fb15ae3274e3981f25cc339469699b406322f97aca","last_reissued_at":"2026-05-18T03:02:44.816135Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:44.816135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representing an element in F_q[t] as the sum of two irreducibles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andreas O. Bender","submitted_at":"2008-09-25T11:33:52Z","abstract_excerpt":"A monic polynomial in F_q[t] of degree n over a finite field F_q of odd characteristic can be written as the sum of two irreducible monic elements in F_q[t] of degrees n and n-1 if q is larger than a bound depending only on n. The main tool is a sufficient condition for simultaneous primality of two polynomials in one variable x with coefficients in F_q[t]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4381","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":"0809.4381","created_at":"2026-05-18T03:02:44.816244+00:00"},{"alias_kind":"arxiv_version","alias_value":"0809.4381v2","created_at":"2026-05-18T03:02:44.816244+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.4381","created_at":"2026-05-18T03:02:44.816244+00:00"},{"alias_kind":"pith_short_12","alias_value":"3S343FNHSVAK","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"3S343FNHSVAKJDRK","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"3S343FNH","created_at":"2026-05-18T12:25:56.245647+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/3S343FNHSVAKJDRKST5RLLRSOT","json":"https://pith.science/pith/3S343FNHSVAKJDRKST5RLLRSOT.json","graph_json":"https://pith.science/api/pith-number/3S343FNHSVAKJDRKST5RLLRSOT/graph.json","events_json":"https://pith.science/api/pith-number/3S343FNHSVAKJDRKST5RLLRSOT/events.json","paper":"https://pith.science/paper/3S343FNH"},"agent_actions":{"view_html":"https://pith.science/pith/3S343FNHSVAKJDRKST5RLLRSOT","download_json":"https://pith.science/pith/3S343FNHSVAKJDRKST5RLLRSOT.json","view_paper":"https://pith.science/paper/3S343FNH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0809.4381&json=true","fetch_graph":"https://pith.science/api/pith-number/3S343FNHSVAKJDRKST5RLLRSOT/graph.json","fetch_events":"https://pith.science/api/pith-number/3S343FNHSVAKJDRKST5RLLRSOT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3S343FNHSVAKJDRKST5RLLRSOT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3S343FNHSVAKJDRKST5RLLRSOT/action/storage_attestation","attest_author":"https://pith.science/pith/3S343FNHSVAKJDRKST5RLLRSOT/action/author_attestation","sign_citation":"https://pith.science/pith/3S343FNHSVAKJDRKST5RLLRSOT/action/citation_signature","submit_replication":"https://pith.science/pith/3S343FNHSVAKJDRKST5RLLRSOT/action/replication_record"}},"created_at":"2026-05-18T03:02:44.816244+00:00","updated_at":"2026-05-18T03:02:44.816244+00:00"}