{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SK5APGSLIHBVCMAKJBCMX4VQQ2","short_pith_number":"pith:SK5APGSL","schema_version":"1.0","canonical_sha256":"92ba079a4b41c351300a4844cbf2b0868d955cf2a5a1d21d6fdec5aeafb832b8","source":{"kind":"arxiv","id":"1703.04193","version":1},"attestation_state":"computed","paper":{"title":"Generators and relations for the shallow mod 2 Hecke algebra in levels $\\Gamma_{0}(3)$ and $\\Gamma_{0}(5)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul Monsky","submitted_at":"2017-03-12T23:05:05Z","abstract_excerpt":"Let $M(\\mathit{odd})\\subset Z/2[[x]]$ be the space of odd mod~2 modular forms of level $\\Gamma_{0}(3)$. It is known that the formal Hecke operators $T_{p}:Z/2[[x]]\\rightarrow Z/2[[x]]$, $p$ an odd prime other than $3$, stabilize $M(\\mathit{odd})$ and act locally nilpotently on it. So $M(\\mathit{odd})$ is an $\\mathcal{O} = Z/2[[t_{5},t_{7}, t_{11}, t_{13}]]$-module with $t_{p}$ acting by $T_{p}$, $p\\in \\{5,7,11,13\\}$. We show:\n  (1) Each $T_{p}:M(\\mathit{odd})\\rightarrow M(\\mathit{odd})$, $p\\ne 3$, is multiplication by some $u$ in the maximal ideal, $m$, of $\\mathcal{O}$.\n  (2) The kernel, $I$,"},"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":"1703.04193","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-12T23:05:05Z","cross_cats_sorted":[],"title_canon_sha256":"98ff0c0489084700952af3561de8aa867ed3e7b771018d4512719f444d4f59ca","abstract_canon_sha256":"1289057fe4eb2d573675e50c12eda4452da186c904cddca43f3ba0c55df7b1a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:49.505661Z","signature_b64":"Fn1MMKm/LPu/gPji/686czDTx6UqaltNWrXWHJDpeQ+644y7bkD7BPKDTANBELUmNJZm176g0S6MvCiOLBytBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92ba079a4b41c351300a4844cbf2b0868d955cf2a5a1d21d6fdec5aeafb832b8","last_reissued_at":"2026-05-18T00:48:49.504865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:49.504865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generators and relations for the shallow mod 2 Hecke algebra in levels $\\Gamma_{0}(3)$ and $\\Gamma_{0}(5)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul Monsky","submitted_at":"2017-03-12T23:05:05Z","abstract_excerpt":"Let $M(\\mathit{odd})\\subset Z/2[[x]]$ be the space of odd mod~2 modular forms of level $\\Gamma_{0}(3)$. It is known that the formal Hecke operators $T_{p}:Z/2[[x]]\\rightarrow Z/2[[x]]$, $p$ an odd prime other than $3$, stabilize $M(\\mathit{odd})$ and act locally nilpotently on it. So $M(\\mathit{odd})$ is an $\\mathcal{O} = Z/2[[t_{5},t_{7}, t_{11}, t_{13}]]$-module with $t_{p}$ acting by $T_{p}$, $p\\in \\{5,7,11,13\\}$. We show:\n  (1) Each $T_{p}:M(\\mathit{odd})\\rightarrow M(\\mathit{odd})$, $p\\ne 3$, is multiplication by some $u$ in the maximal ideal, $m$, of $\\mathcal{O}$.\n  (2) The kernel, $I$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04193","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":"1703.04193","created_at":"2026-05-18T00:48:49.504995+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.04193v1","created_at":"2026-05-18T00:48:49.504995+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04193","created_at":"2026-05-18T00:48:49.504995+00:00"},{"alias_kind":"pith_short_12","alias_value":"SK5APGSLIHBV","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SK5APGSLIHBVCMAK","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SK5APGSL","created_at":"2026-05-18T12:31:43.269735+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/SK5APGSLIHBVCMAKJBCMX4VQQ2","json":"https://pith.science/pith/SK5APGSLIHBVCMAKJBCMX4VQQ2.json","graph_json":"https://pith.science/api/pith-number/SK5APGSLIHBVCMAKJBCMX4VQQ2/graph.json","events_json":"https://pith.science/api/pith-number/SK5APGSLIHBVCMAKJBCMX4VQQ2/events.json","paper":"https://pith.science/paper/SK5APGSL"},"agent_actions":{"view_html":"https://pith.science/pith/SK5APGSLIHBVCMAKJBCMX4VQQ2","download_json":"https://pith.science/pith/SK5APGSLIHBVCMAKJBCMX4VQQ2.json","view_paper":"https://pith.science/paper/SK5APGSL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.04193&json=true","fetch_graph":"https://pith.science/api/pith-number/SK5APGSLIHBVCMAKJBCMX4VQQ2/graph.json","fetch_events":"https://pith.science/api/pith-number/SK5APGSLIHBVCMAKJBCMX4VQQ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SK5APGSLIHBVCMAKJBCMX4VQQ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SK5APGSLIHBVCMAKJBCMX4VQQ2/action/storage_attestation","attest_author":"https://pith.science/pith/SK5APGSLIHBVCMAKJBCMX4VQQ2/action/author_attestation","sign_citation":"https://pith.science/pith/SK5APGSLIHBVCMAKJBCMX4VQQ2/action/citation_signature","submit_replication":"https://pith.science/pith/SK5APGSLIHBVCMAKJBCMX4VQQ2/action/replication_record"}},"created_at":"2026-05-18T00:48:49.504995+00:00","updated_at":"2026-05-18T00:48:49.504995+00:00"}