{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:2ZC5FJFTEU2GLE2C4472BICJ2B","short_pith_number":"pith:2ZC5FJFT","schema_version":"1.0","canonical_sha256":"d645d2a4b32534659342e73fa0a049d058f1325f21d865701f75415db1c501db","source":{"kind":"arxiv","id":"1307.0169","version":1},"attestation_state":"computed","paper":{"title":"Classification of congruences for mock theta functions and weakly holomorphic modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nickolas Andersen","submitted_at":"2013-06-30T02:00:25Z","abstract_excerpt":"Let $f(q)$ denote Ramanujan's mock theta function \\[f(q) = \\sum_{n=0}^{\\infty} a(n) q^{n} := 1+\\sum_{n=1}^{\\infty} \\frac{q^{n^{2}}}{(1+q)^{2}(1+q^{2})^{2}\\cdots(1+q^{n})^{2}}.\\] It is known that there are many linear congruences for the coefficients of $f(q)$ and other mock theta functions. We prove that if the linear congruence $a(mn+t) \\equiv 0 \\pmod{\\ell}$ holds for some prime $\\ell \\geq 5$, then $\\ell | m$ and $(\\frac{24t-1}{\\ell}) \\neq (\\frac{-1}{\\ell})$. We prove analogous results for the mock theta function $\\omega(q)$ and for a large class of weakly holomorphic modular forms which incl"},"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":"1307.0169","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-06-30T02:00:25Z","cross_cats_sorted":[],"title_canon_sha256":"f31de827f898f82bda5fdcb96382228b42911719d8599c124a69f6c329d5c0ec","abstract_canon_sha256":"b8f01135ae6941adcaf880893dcb6d0172daeefb40d5668f5024869bc9510eb7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:52.045046Z","signature_b64":"tXSgV4MSRvgfk4acl7HLpf7E5GiXpsQ06vggYLSp9A5vQkO/RviYS3z/IBd2+0LouuyejOiJQOszSjUHAzL3BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d645d2a4b32534659342e73fa0a049d058f1325f21d865701f75415db1c501db","last_reissued_at":"2026-05-18T02:18:52.044415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:52.044415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of congruences for mock theta functions and weakly holomorphic modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nickolas Andersen","submitted_at":"2013-06-30T02:00:25Z","abstract_excerpt":"Let $f(q)$ denote Ramanujan's mock theta function \\[f(q) = \\sum_{n=0}^{\\infty} a(n) q^{n} := 1+\\sum_{n=1}^{\\infty} \\frac{q^{n^{2}}}{(1+q)^{2}(1+q^{2})^{2}\\cdots(1+q^{n})^{2}}.\\] It is known that there are many linear congruences for the coefficients of $f(q)$ and other mock theta functions. We prove that if the linear congruence $a(mn+t) \\equiv 0 \\pmod{\\ell}$ holds for some prime $\\ell \\geq 5$, then $\\ell | m$ and $(\\frac{24t-1}{\\ell}) \\neq (\\frac{-1}{\\ell})$. We prove analogous results for the mock theta function $\\omega(q)$ and for a large class of weakly holomorphic modular forms which incl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0169","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":"1307.0169","created_at":"2026-05-18T02:18:52.044515+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.0169v1","created_at":"2026-05-18T02:18:52.044515+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0169","created_at":"2026-05-18T02:18:52.044515+00:00"},{"alias_kind":"pith_short_12","alias_value":"2ZC5FJFTEU2G","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"2ZC5FJFTEU2GLE2C","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"2ZC5FJFT","created_at":"2026-05-18T12:27:32.513160+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/2ZC5FJFTEU2GLE2C4472BICJ2B","json":"https://pith.science/pith/2ZC5FJFTEU2GLE2C4472BICJ2B.json","graph_json":"https://pith.science/api/pith-number/2ZC5FJFTEU2GLE2C4472BICJ2B/graph.json","events_json":"https://pith.science/api/pith-number/2ZC5FJFTEU2GLE2C4472BICJ2B/events.json","paper":"https://pith.science/paper/2ZC5FJFT"},"agent_actions":{"view_html":"https://pith.science/pith/2ZC5FJFTEU2GLE2C4472BICJ2B","download_json":"https://pith.science/pith/2ZC5FJFTEU2GLE2C4472BICJ2B.json","view_paper":"https://pith.science/paper/2ZC5FJFT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.0169&json=true","fetch_graph":"https://pith.science/api/pith-number/2ZC5FJFTEU2GLE2C4472BICJ2B/graph.json","fetch_events":"https://pith.science/api/pith-number/2ZC5FJFTEU2GLE2C4472BICJ2B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2ZC5FJFTEU2GLE2C4472BICJ2B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2ZC5FJFTEU2GLE2C4472BICJ2B/action/storage_attestation","attest_author":"https://pith.science/pith/2ZC5FJFTEU2GLE2C4472BICJ2B/action/author_attestation","sign_citation":"https://pith.science/pith/2ZC5FJFTEU2GLE2C4472BICJ2B/action/citation_signature","submit_replication":"https://pith.science/pith/2ZC5FJFTEU2GLE2C4472BICJ2B/action/replication_record"}},"created_at":"2026-05-18T02:18:52.044515+00:00","updated_at":"2026-05-18T02:18:52.044515+00:00"}