{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:RTAU2DGSYQYS4B4VHAOTPOXAPJ","short_pith_number":"pith:RTAU2DGS","schema_version":"1.0","canonical_sha256":"8cc14d0cd2c4312e0795381d37bae07a404e7916033e06ad37aa4b6144b35260","source":{"kind":"arxiv","id":"1311.3043","version":1},"attestation_state":"computed","paper":{"title":"Renormalization and quantum modular forms, part I: Maass wave forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hieu T. Ngo, Robert C. Rhoades, Yingkun Li","submitted_at":"2013-11-13T08:02:46Z","abstract_excerpt":"Sander Zwegers showed that Ramanujan's mock theta functions are $q$-hypergeometric series, whose $q$-expansion coefficients are half of the Fourier coefficients of a non-holomorphic modular form. George Andrews, Henri Cohen, Freeman Dyson, and Dean Hickerson found a pair of $q$-hypergeometric series each of which contains half of the Fourier coefficients of Maass waveform of eigenvalue $1/4$.\n  This series of papers shows that a $q$-series construction, called ``renormalization'', yields the other half of the Fourier coefficients from a series which contains half of them. This construction uni"},"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":"1311.3043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-13T08:02:46Z","cross_cats_sorted":[],"title_canon_sha256":"e6db60b313a3507891903353b0e2b063f0733aa7a84ea6d8313825f170d6f260","abstract_canon_sha256":"51ced4cbc554a7c339d0b3ef3cc8b36f67a0fee10df59e234e63711e70560e0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:13.282037Z","signature_b64":"ZTMR4AlKHEgduNELsHFgMt+G8q3OVgCpFKYcSNX25kMvPAFiFrhiArJB7dajSVFGkkVcxvO04QfpeYDALUpMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cc14d0cd2c4312e0795381d37bae07a404e7916033e06ad37aa4b6144b35260","last_reissued_at":"2026-05-18T03:07:13.281561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:13.281561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Renormalization and quantum modular forms, part I: Maass wave forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hieu T. Ngo, Robert C. Rhoades, Yingkun Li","submitted_at":"2013-11-13T08:02:46Z","abstract_excerpt":"Sander Zwegers showed that Ramanujan's mock theta functions are $q$-hypergeometric series, whose $q$-expansion coefficients are half of the Fourier coefficients of a non-holomorphic modular form. George Andrews, Henri Cohen, Freeman Dyson, and Dean Hickerson found a pair of $q$-hypergeometric series each of which contains half of the Fourier coefficients of Maass waveform of eigenvalue $1/4$.\n  This series of papers shows that a $q$-series construction, called ``renormalization'', yields the other half of the Fourier coefficients from a series which contains half of them. This construction uni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3043","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":"1311.3043","created_at":"2026-05-18T03:07:13.281641+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.3043v1","created_at":"2026-05-18T03:07:13.281641+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3043","created_at":"2026-05-18T03:07:13.281641+00:00"},{"alias_kind":"pith_short_12","alias_value":"RTAU2DGSYQYS","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"RTAU2DGSYQYS4B4V","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"RTAU2DGS","created_at":"2026-05-18T12:27:59.945178+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/RTAU2DGSYQYS4B4VHAOTPOXAPJ","json":"https://pith.science/pith/RTAU2DGSYQYS4B4VHAOTPOXAPJ.json","graph_json":"https://pith.science/api/pith-number/RTAU2DGSYQYS4B4VHAOTPOXAPJ/graph.json","events_json":"https://pith.science/api/pith-number/RTAU2DGSYQYS4B4VHAOTPOXAPJ/events.json","paper":"https://pith.science/paper/RTAU2DGS"},"agent_actions":{"view_html":"https://pith.science/pith/RTAU2DGSYQYS4B4VHAOTPOXAPJ","download_json":"https://pith.science/pith/RTAU2DGSYQYS4B4VHAOTPOXAPJ.json","view_paper":"https://pith.science/paper/RTAU2DGS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.3043&json=true","fetch_graph":"https://pith.science/api/pith-number/RTAU2DGSYQYS4B4VHAOTPOXAPJ/graph.json","fetch_events":"https://pith.science/api/pith-number/RTAU2DGSYQYS4B4VHAOTPOXAPJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RTAU2DGSYQYS4B4VHAOTPOXAPJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RTAU2DGSYQYS4B4VHAOTPOXAPJ/action/storage_attestation","attest_author":"https://pith.science/pith/RTAU2DGSYQYS4B4VHAOTPOXAPJ/action/author_attestation","sign_citation":"https://pith.science/pith/RTAU2DGSYQYS4B4VHAOTPOXAPJ/action/citation_signature","submit_replication":"https://pith.science/pith/RTAU2DGSYQYS4B4VHAOTPOXAPJ/action/replication_record"}},"created_at":"2026-05-18T03:07:13.281641+00:00","updated_at":"2026-05-18T03:07:13.281641+00:00"}