{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:X2LRBD4IZVNAJEO4PDA5A6K4RG","short_pith_number":"pith:X2LRBD4I","schema_version":"1.0","canonical_sha256":"be97108f88cd5a0491dc78c1d0795c89b4eda912bcf5c90223e9f66dec710371","source":{"kind":"arxiv","id":"1508.07523","version":2},"attestation_state":"computed","paper":{"title":"A Hecke algebra attached to mod 2 modular forms of level 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul Monsky","submitted_at":"2015-08-30T02:04:00Z","abstract_excerpt":"Let $D$ in $Z/2[[x]]$ be $\\sum x^{n^{2}}$, $n>0$ and prime to $6$. Let $W$ be spanned by the $D^{k}$, $k>0$ and prime to $6$. Then the formal Hecke operators $T_{p}$, $p>3$, stabilize $W$, and it can be shown that they act locally nilpotently. We show that the completion of the Hecke algebra generated by these $T_{p}$ acting on $W$, with respect to the maximal ideal generated by the $T_{p}$, is a power series ring in $T_{7}$ and $T_{13}$ with an element of square $0$ adjoined. This may be viewed as a level 3 analog of the level 1 results of Nicolas and Serre -- the Hecke stable space they stud"},"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":"1508.07523","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-30T02:04:00Z","cross_cats_sorted":[],"title_canon_sha256":"b24d98d31cac9a2f02401aed6072a3ac1a63bb619c0552ebe784375b79cd4ef6","abstract_canon_sha256":"e76e1edef5d0bf04c7cfb5c1d15b32eb54b7b4dcf2ada440b6e381b7624e4670"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:56.849341Z","signature_b64":"ea2tUHg6D8e+ZuUCC+/TjoDDZmsGZf1v4YEzqfMxwy8sdwRpZE83vLz8DIv9CZGNew7WO8F5Pc22M3Pjws6GDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be97108f88cd5a0491dc78c1d0795c89b4eda912bcf5c90223e9f66dec710371","last_reissued_at":"2026-05-18T01:02:56.848753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:56.848753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Hecke algebra attached to mod 2 modular forms of level 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul Monsky","submitted_at":"2015-08-30T02:04:00Z","abstract_excerpt":"Let $D$ in $Z/2[[x]]$ be $\\sum x^{n^{2}}$, $n>0$ and prime to $6$. Let $W$ be spanned by the $D^{k}$, $k>0$ and prime to $6$. Then the formal Hecke operators $T_{p}$, $p>3$, stabilize $W$, and it can be shown that they act locally nilpotently. We show that the completion of the Hecke algebra generated by these $T_{p}$ acting on $W$, with respect to the maximal ideal generated by the $T_{p}$, is a power series ring in $T_{7}$ and $T_{13}$ with an element of square $0$ adjoined. This may be viewed as a level 3 analog of the level 1 results of Nicolas and Serre -- the Hecke stable space they stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07523","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":"1508.07523","created_at":"2026-05-18T01:02:56.848865+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.07523v2","created_at":"2026-05-18T01:02:56.848865+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07523","created_at":"2026-05-18T01:02:56.848865+00:00"},{"alias_kind":"pith_short_12","alias_value":"X2LRBD4IZVNA","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"X2LRBD4IZVNAJEO4","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"X2LRBD4I","created_at":"2026-05-18T12:29:47.479230+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/X2LRBD4IZVNAJEO4PDA5A6K4RG","json":"https://pith.science/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG.json","graph_json":"https://pith.science/api/pith-number/X2LRBD4IZVNAJEO4PDA5A6K4RG/graph.json","events_json":"https://pith.science/api/pith-number/X2LRBD4IZVNAJEO4PDA5A6K4RG/events.json","paper":"https://pith.science/paper/X2LRBD4I"},"agent_actions":{"view_html":"https://pith.science/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG","download_json":"https://pith.science/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG.json","view_paper":"https://pith.science/paper/X2LRBD4I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.07523&json=true","fetch_graph":"https://pith.science/api/pith-number/X2LRBD4IZVNAJEO4PDA5A6K4RG/graph.json","fetch_events":"https://pith.science/api/pith-number/X2LRBD4IZVNAJEO4PDA5A6K4RG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG/action/storage_attestation","attest_author":"https://pith.science/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG/action/author_attestation","sign_citation":"https://pith.science/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG/action/citation_signature","submit_replication":"https://pith.science/pith/X2LRBD4IZVNAJEO4PDA5A6K4RG/action/replication_record"}},"created_at":"2026-05-18T01:02:56.848865+00:00","updated_at":"2026-05-18T01:02:56.848865+00:00"}