{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QHXVVF5SLVFOLCHBD7PSMFNL2H","short_pith_number":"pith:QHXVVF5S","schema_version":"1.0","canonical_sha256":"81ef5a97b25d4ae588e11fdf2615abd1d1af06077abe278e3b0b96440f3de73f","source":{"kind":"arxiv","id":"1404.6281","version":2},"attestation_state":"computed","paper":{"title":"Explicit factorization of $x^n-1\\in \\mathbb F_q[x]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NT"],"primary_cat":"cs.IT","authors_text":"C. R. Giraldo Vergara, F.E. Brochero Mart\\'inez, L. Batista de Oliveira","submitted_at":"2014-04-24T22:19:08Z","abstract_excerpt":"Let $\\mathbb F_q$ be a finite field and $n$ a positive integer. In this article, we prove that, under some conditions on $q$ and $n$, the polynomial $x^n-1$ can be split into irreducible binomials $x^t-a$ and an explicit factorization into irreducible factors is given.\n  Finally, weakening one of our hypothesis, we also obtain factors of the form $x^{2t}-ax^t+b$ and explicit splitting of $x^n-1$ into irreducible factors is given."},"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":"1404.6281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-04-24T22:19:08Z","cross_cats_sorted":["math.IT","math.NT"],"title_canon_sha256":"d39802e4ae193fba4c645e1df14196869339ba4194ffa02ed13afdd471814aa2","abstract_canon_sha256":"76b72ef9b3526a260e5fff61083ea610de6d0951e9f0db4487ee1a46e4ff5327"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:41.352190Z","signature_b64":"51IBM8+EbuHC093uxZJRDfGwY5cMdxhWQl5FMRdSO/OFM/TFotjRVWkr+cfos8URoCjTOiVsKoUrpENiFJTbDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81ef5a97b25d4ae588e11fdf2615abd1d1af06077abe278e3b0b96440f3de73f","last_reissued_at":"2026-05-18T02:51:41.351713Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:41.351713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit factorization of $x^n-1\\in \\mathbb F_q[x]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NT"],"primary_cat":"cs.IT","authors_text":"C. R. Giraldo Vergara, F.E. Brochero Mart\\'inez, L. Batista de Oliveira","submitted_at":"2014-04-24T22:19:08Z","abstract_excerpt":"Let $\\mathbb F_q$ be a finite field and $n$ a positive integer. In this article, we prove that, under some conditions on $q$ and $n$, the polynomial $x^n-1$ can be split into irreducible binomials $x^t-a$ and an explicit factorization into irreducible factors is given.\n  Finally, weakening one of our hypothesis, we also obtain factors of the form $x^{2t}-ax^t+b$ and explicit splitting of $x^n-1$ into irreducible factors is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6281","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":"1404.6281","created_at":"2026-05-18T02:51:41.351781+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.6281v2","created_at":"2026-05-18T02:51:41.351781+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6281","created_at":"2026-05-18T02:51:41.351781+00:00"},{"alias_kind":"pith_short_12","alias_value":"QHXVVF5SLVFO","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"QHXVVF5SLVFOLCHB","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"QHXVVF5S","created_at":"2026-05-18T12:28:46.137349+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/QHXVVF5SLVFOLCHBD7PSMFNL2H","json":"https://pith.science/pith/QHXVVF5SLVFOLCHBD7PSMFNL2H.json","graph_json":"https://pith.science/api/pith-number/QHXVVF5SLVFOLCHBD7PSMFNL2H/graph.json","events_json":"https://pith.science/api/pith-number/QHXVVF5SLVFOLCHBD7PSMFNL2H/events.json","paper":"https://pith.science/paper/QHXVVF5S"},"agent_actions":{"view_html":"https://pith.science/pith/QHXVVF5SLVFOLCHBD7PSMFNL2H","download_json":"https://pith.science/pith/QHXVVF5SLVFOLCHBD7PSMFNL2H.json","view_paper":"https://pith.science/paper/QHXVVF5S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.6281&json=true","fetch_graph":"https://pith.science/api/pith-number/QHXVVF5SLVFOLCHBD7PSMFNL2H/graph.json","fetch_events":"https://pith.science/api/pith-number/QHXVVF5SLVFOLCHBD7PSMFNL2H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QHXVVF5SLVFOLCHBD7PSMFNL2H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QHXVVF5SLVFOLCHBD7PSMFNL2H/action/storage_attestation","attest_author":"https://pith.science/pith/QHXVVF5SLVFOLCHBD7PSMFNL2H/action/author_attestation","sign_citation":"https://pith.science/pith/QHXVVF5SLVFOLCHBD7PSMFNL2H/action/citation_signature","submit_replication":"https://pith.science/pith/QHXVVF5SLVFOLCHBD7PSMFNL2H/action/replication_record"}},"created_at":"2026-05-18T02:51:41.351781+00:00","updated_at":"2026-05-18T02:51:41.351781+00:00"}