{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NVG4TCY7TQJXGPUDUZJSORW42G","short_pith_number":"pith:NVG4TCY7","schema_version":"1.0","canonical_sha256":"6d4dc98b1f9c13733e83a6532746dcd1817daeed10a9d3b606256245c017568a","source":{"kind":"arxiv","id":"1604.02622","version":2},"attestation_state":"computed","paper":{"title":"Variations on a Lemma of Nicolas and Serre","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul Monsky","submitted_at":"2016-04-10T00:49:12Z","abstract_excerpt":"The \"Nicolas-Serre code\", $(a,b) \\leftrightarrow t^{n}$, is a bijection between $N\\times N$ and those $t^{n}$, $n$ odd, in $Z/2[t]$. Suppose $A_{n}$, $n$ odd, in $Z/2[t]$ are defined by: $A_{1}= A_{5}= 0$, $A_{3}= t$, $A_{7}= t^{5}$, and $A_{n+8}= t^{8} A_{n} + t^{2} A_{n+2}$. A lemma, Proposition 4.3 of [6], used to study the Hecke algebra attached to the space of mod $2$ level $1$ modular forms, gives information about the codes $(a,b)$ attached to the monomials appearing in $A_{n}$. The unpublished highly technical proof has been simplified by Gerbelli-Gauthier.\n  Our Theorem 3.7 generalize"},"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":"1604.02622","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-10T00:49:12Z","cross_cats_sorted":[],"title_canon_sha256":"ff843cb392087fadaedc4199bd8bcbab83320c880a5007358189a71851e28b75","abstract_canon_sha256":"711f792ef7ed0c5ff874c10b81262d219ea4c9daa0c520533ef2c5893cc8f307"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:28.530497Z","signature_b64":"JS3y4QUL9/LRZtil0f/+0xOl8nAXsXS78ieXfGi3tSpfrgJGcwXGmhka67yXff9hLY2Q32Xh59U1hifVzP9SBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d4dc98b1f9c13733e83a6532746dcd1817daeed10a9d3b606256245c017568a","last_reissued_at":"2026-05-18T00:55:28.529857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:28.529857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Variations on a Lemma of Nicolas and Serre","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul Monsky","submitted_at":"2016-04-10T00:49:12Z","abstract_excerpt":"The \"Nicolas-Serre code\", $(a,b) \\leftrightarrow t^{n}$, is a bijection between $N\\times N$ and those $t^{n}$, $n$ odd, in $Z/2[t]$. Suppose $A_{n}$, $n$ odd, in $Z/2[t]$ are defined by: $A_{1}= A_{5}= 0$, $A_{3}= t$, $A_{7}= t^{5}$, and $A_{n+8}= t^{8} A_{n} + t^{2} A_{n+2}$. A lemma, Proposition 4.3 of [6], used to study the Hecke algebra attached to the space of mod $2$ level $1$ modular forms, gives information about the codes $(a,b)$ attached to the monomials appearing in $A_{n}$. The unpublished highly technical proof has been simplified by Gerbelli-Gauthier.\n  Our Theorem 3.7 generalize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02622","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":"1604.02622","created_at":"2026-05-18T00:55:28.529946+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.02622v2","created_at":"2026-05-18T00:55:28.529946+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02622","created_at":"2026-05-18T00:55:28.529946+00:00"},{"alias_kind":"pith_short_12","alias_value":"NVG4TCY7TQJX","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"NVG4TCY7TQJXGPUD","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"NVG4TCY7","created_at":"2026-05-18T12:30:36.002864+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/NVG4TCY7TQJXGPUDUZJSORW42G","json":"https://pith.science/pith/NVG4TCY7TQJXGPUDUZJSORW42G.json","graph_json":"https://pith.science/api/pith-number/NVG4TCY7TQJXGPUDUZJSORW42G/graph.json","events_json":"https://pith.science/api/pith-number/NVG4TCY7TQJXGPUDUZJSORW42G/events.json","paper":"https://pith.science/paper/NVG4TCY7"},"agent_actions":{"view_html":"https://pith.science/pith/NVG4TCY7TQJXGPUDUZJSORW42G","download_json":"https://pith.science/pith/NVG4TCY7TQJXGPUDUZJSORW42G.json","view_paper":"https://pith.science/paper/NVG4TCY7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.02622&json=true","fetch_graph":"https://pith.science/api/pith-number/NVG4TCY7TQJXGPUDUZJSORW42G/graph.json","fetch_events":"https://pith.science/api/pith-number/NVG4TCY7TQJXGPUDUZJSORW42G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NVG4TCY7TQJXGPUDUZJSORW42G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NVG4TCY7TQJXGPUDUZJSORW42G/action/storage_attestation","attest_author":"https://pith.science/pith/NVG4TCY7TQJXGPUDUZJSORW42G/action/author_attestation","sign_citation":"https://pith.science/pith/NVG4TCY7TQJXGPUDUZJSORW42G/action/citation_signature","submit_replication":"https://pith.science/pith/NVG4TCY7TQJXGPUDUZJSORW42G/action/replication_record"}},"created_at":"2026-05-18T00:55:28.529946+00:00","updated_at":"2026-05-18T00:55:28.529946+00:00"}