{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:FQC2KOCVA7UA3JLSYYS7AAI6JY","short_pith_number":"pith:FQC2KOCV","schema_version":"1.0","canonical_sha256":"2c05a5385507e80da572c625f0011e4e0782c7b72e746d8415a5a20beb455f93","source":{"kind":"arxiv","id":"1007.0326","version":1},"attestation_state":"computed","paper":{"title":"Construction of Self-Dual Integral Normal Bases in Abelian Extensions of Finite and Local Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Erik Jarl Pickett","submitted_at":"2010-07-02T09:59:30Z","abstract_excerpt":"Let $F/E$ be a finite Galois extension of fields with abelian Galois group $\\Gamma$. A self-dual normal basis for $F/E$ is a normal basis with the additional property that $Tr_{F/E}(g(x),h(x))=\\delta_{g,h}$ for $g,h\\in\\Gamma$. Bayer-Fluckiger and Lenstra have shown that when $char(E)\\neq 2$, then $F$ admits a self-dual normal basis if and only if $[F:E]$ is odd. If $F/E$ is an extension of finite fields and $char(E)=2$, then $F$ admits a self-dual normal basis if and only if the exponent of $\\Gamma$ is not divisible by $4$. In this paper we construct self-dual normal basis generators for finit"},"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":"1007.0326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-07-02T09:59:30Z","cross_cats_sorted":[],"title_canon_sha256":"7af7672c68c2d4247320dab2c0b69384b65994a3082005e9b6f7b0286cc990bc","abstract_canon_sha256":"6d578119137dafa15a24b356da1f249ae43686ead6bcbc78af4f0d23022c8a8e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:48.371508Z","signature_b64":"yakPbGYZTiKf0P45IIGgKFb7qMu8C4Uhm3LaZeZiOB8kaR3o1gZVay7IEKxOH4QUbwAvjP3lGXaHGBabLny+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c05a5385507e80da572c625f0011e4e0782c7b72e746d8415a5a20beb455f93","last_reissued_at":"2026-05-18T04:30:48.371016Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:48.371016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Construction of Self-Dual Integral Normal Bases in Abelian Extensions of Finite and Local Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Erik Jarl Pickett","submitted_at":"2010-07-02T09:59:30Z","abstract_excerpt":"Let $F/E$ be a finite Galois extension of fields with abelian Galois group $\\Gamma$. A self-dual normal basis for $F/E$ is a normal basis with the additional property that $Tr_{F/E}(g(x),h(x))=\\delta_{g,h}$ for $g,h\\in\\Gamma$. Bayer-Fluckiger and Lenstra have shown that when $char(E)\\neq 2$, then $F$ admits a self-dual normal basis if and only if $[F:E]$ is odd. If $F/E$ is an extension of finite fields and $char(E)=2$, then $F$ admits a self-dual normal basis if and only if the exponent of $\\Gamma$ is not divisible by $4$. In this paper we construct self-dual normal basis generators for finit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0326","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":"1007.0326","created_at":"2026-05-18T04:30:48.371102+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.0326v1","created_at":"2026-05-18T04:30:48.371102+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0326","created_at":"2026-05-18T04:30:48.371102+00:00"},{"alias_kind":"pith_short_12","alias_value":"FQC2KOCVA7UA","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"FQC2KOCVA7UA3JLS","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"FQC2KOCV","created_at":"2026-05-18T12:26:07.630475+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/FQC2KOCVA7UA3JLSYYS7AAI6JY","json":"https://pith.science/pith/FQC2KOCVA7UA3JLSYYS7AAI6JY.json","graph_json":"https://pith.science/api/pith-number/FQC2KOCVA7UA3JLSYYS7AAI6JY/graph.json","events_json":"https://pith.science/api/pith-number/FQC2KOCVA7UA3JLSYYS7AAI6JY/events.json","paper":"https://pith.science/paper/FQC2KOCV"},"agent_actions":{"view_html":"https://pith.science/pith/FQC2KOCVA7UA3JLSYYS7AAI6JY","download_json":"https://pith.science/pith/FQC2KOCVA7UA3JLSYYS7AAI6JY.json","view_paper":"https://pith.science/paper/FQC2KOCV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.0326&json=true","fetch_graph":"https://pith.science/api/pith-number/FQC2KOCVA7UA3JLSYYS7AAI6JY/graph.json","fetch_events":"https://pith.science/api/pith-number/FQC2KOCVA7UA3JLSYYS7AAI6JY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FQC2KOCVA7UA3JLSYYS7AAI6JY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FQC2KOCVA7UA3JLSYYS7AAI6JY/action/storage_attestation","attest_author":"https://pith.science/pith/FQC2KOCVA7UA3JLSYYS7AAI6JY/action/author_attestation","sign_citation":"https://pith.science/pith/FQC2KOCVA7UA3JLSYYS7AAI6JY/action/citation_signature","submit_replication":"https://pith.science/pith/FQC2KOCVA7UA3JLSYYS7AAI6JY/action/replication_record"}},"created_at":"2026-05-18T04:30:48.371102+00:00","updated_at":"2026-05-18T04:30:48.371102+00:00"}