{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:SELVO6J3XMYZF4CLFBJFA4IF6Q","short_pith_number":"pith:SELVO6J3","schema_version":"1.0","canonical_sha256":"911757793bbb3192f04b2852507105f40885cc2223bfb00ff92912972d1b66ec","source":{"kind":"arxiv","id":"1311.2154","version":1},"attestation_state":"computed","paper":{"title":"The compositional inverses of linearized permutation binomials over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Baofeng Wu","submitted_at":"2013-11-09T09:30:04Z","abstract_excerpt":"Let $q$ be a prime power and $n$ and $r$ be positive integers. It is well known that the linearized binomial $L_r(x)=x^{q^r}+ax\\in\\mathbb{F}_{q^n}[x]$ is a permutation polynomial if and only if $(-1)^{n/d}a^{{(q^n-1)}/{(q^{d}-1)}}\\neq 1$ where $d=(n,r)$. In this paper, the compositional inverse of $L_r(x)$ is explicitly determined when this condition holds."},"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":"1311.2154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-09T09:30:04Z","cross_cats_sorted":[],"title_canon_sha256":"e3f27f202fa2ba1e9c977de6d9061a676de9493f8194097f9d0623b24cf9ddb1","abstract_canon_sha256":"6409c6a09257f80ff36069516ecdeac1597eafa30ec873071e416424badedb9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:33.375024Z","signature_b64":"LKfz59uyIhbZRKbJNFBEUEiJFu6n4DxrMvX6mP9CwlXCUieHqoZ74St9ycSAox/I8Dg/aHQd1nP4qJqOvH1MDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"911757793bbb3192f04b2852507105f40885cc2223bfb00ff92912972d1b66ec","last_reissued_at":"2026-05-18T03:07:33.374281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:33.374281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The compositional inverses of linearized permutation binomials over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Baofeng Wu","submitted_at":"2013-11-09T09:30:04Z","abstract_excerpt":"Let $q$ be a prime power and $n$ and $r$ be positive integers. It is well known that the linearized binomial $L_r(x)=x^{q^r}+ax\\in\\mathbb{F}_{q^n}[x]$ is a permutation polynomial if and only if $(-1)^{n/d}a^{{(q^n-1)}/{(q^{d}-1)}}\\neq 1$ where $d=(n,r)$. In this paper, the compositional inverse of $L_r(x)$ is explicitly determined when this condition holds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2154","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":"1311.2154","created_at":"2026-05-18T03:07:33.374414+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.2154v1","created_at":"2026-05-18T03:07:33.374414+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2154","created_at":"2026-05-18T03:07:33.374414+00:00"},{"alias_kind":"pith_short_12","alias_value":"SELVO6J3XMYZ","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SELVO6J3XMYZF4CL","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SELVO6J3","created_at":"2026-05-18T12:27:59.945178+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/SELVO6J3XMYZF4CLFBJFA4IF6Q","json":"https://pith.science/pith/SELVO6J3XMYZF4CLFBJFA4IF6Q.json","graph_json":"https://pith.science/api/pith-number/SELVO6J3XMYZF4CLFBJFA4IF6Q/graph.json","events_json":"https://pith.science/api/pith-number/SELVO6J3XMYZF4CLFBJFA4IF6Q/events.json","paper":"https://pith.science/paper/SELVO6J3"},"agent_actions":{"view_html":"https://pith.science/pith/SELVO6J3XMYZF4CLFBJFA4IF6Q","download_json":"https://pith.science/pith/SELVO6J3XMYZF4CLFBJFA4IF6Q.json","view_paper":"https://pith.science/paper/SELVO6J3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.2154&json=true","fetch_graph":"https://pith.science/api/pith-number/SELVO6J3XMYZF4CLFBJFA4IF6Q/graph.json","fetch_events":"https://pith.science/api/pith-number/SELVO6J3XMYZF4CLFBJFA4IF6Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SELVO6J3XMYZF4CLFBJFA4IF6Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SELVO6J3XMYZF4CLFBJFA4IF6Q/action/storage_attestation","attest_author":"https://pith.science/pith/SELVO6J3XMYZF4CLFBJFA4IF6Q/action/author_attestation","sign_citation":"https://pith.science/pith/SELVO6J3XMYZF4CLFBJFA4IF6Q/action/citation_signature","submit_replication":"https://pith.science/pith/SELVO6J3XMYZF4CLFBJFA4IF6Q/action/replication_record"}},"created_at":"2026-05-18T03:07:33.374414+00:00","updated_at":"2026-05-18T03:07:33.374414+00:00"}