{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:GQSC6U27JKXSEMDKRNFRIYR4WT","short_pith_number":"pith:GQSC6U27","schema_version":"1.0","canonical_sha256":"34242f535f4aaf22306a8b4b14623cb4e1f127c71c2cd129745f5fd5dc0306f2","source":{"kind":"arxiv","id":"1209.5197","version":2},"attestation_state":"computed","paper":{"title":"Formulas for the coefficients of half-integral weight harmonic Maass forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Claudia Alfes","submitted_at":"2012-09-24T08:57:55Z","abstract_excerpt":"Recently, Bruinier and Ono proved that the coefficients of certain weight -1/2 harmonic weak Maa{\\ss} forms are given as \"traces\" of singular moduli for harmonic weak Maa{\\ss} forms. Here, we prove that similar results hold for the coefficients of harmonic weak Maa{\\ss} forms of weight $3/2+k$, $k$ even, and weight $1/2-k$, $k$ odd, by extending the theta lift of Bruinier-Funke and Bruinier-Ono. Moreover, we generalize their result to include \\textit{twisted} traces of singular moduli using earlier work of the author and Ehlen. Employing a duality result between weight $k$ and $2-k$, we are ab"},"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":"1209.5197","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-24T08:57:55Z","cross_cats_sorted":[],"title_canon_sha256":"eb3f8e71fb20bee1a8207aaf1623961c4618377a41f0a4d7f431bb5116ea8c00","abstract_canon_sha256":"ed7990cbfbf40f540237fd34fb33da3ce02f6eacc5030b0caed8a955b15171f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:39.825684Z","signature_b64":"PfIaQGn5M+kkTG5WuPMeFxwXX0DbbpNXnuZ8avAzc5lLgvdHUNFzJ7WTJBeqfqRZl8EYxjm3ucsQLdvi9ClpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34242f535f4aaf22306a8b4b14623cb4e1f127c71c2cd129745f5fd5dc0306f2","last_reissued_at":"2026-05-18T03:43:39.825045Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:39.825045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Formulas for the coefficients of half-integral weight harmonic Maass forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Claudia Alfes","submitted_at":"2012-09-24T08:57:55Z","abstract_excerpt":"Recently, Bruinier and Ono proved that the coefficients of certain weight -1/2 harmonic weak Maa{\\ss} forms are given as \"traces\" of singular moduli for harmonic weak Maa{\\ss} forms. Here, we prove that similar results hold for the coefficients of harmonic weak Maa{\\ss} forms of weight $3/2+k$, $k$ even, and weight $1/2-k$, $k$ odd, by extending the theta lift of Bruinier-Funke and Bruinier-Ono. Moreover, we generalize their result to include \\textit{twisted} traces of singular moduli using earlier work of the author and Ehlen. Employing a duality result between weight $k$ and $2-k$, we are ab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5197","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":"1209.5197","created_at":"2026-05-18T03:43:39.825140+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.5197v2","created_at":"2026-05-18T03:43:39.825140+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5197","created_at":"2026-05-18T03:43:39.825140+00:00"},{"alias_kind":"pith_short_12","alias_value":"GQSC6U27JKXS","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"GQSC6U27JKXSEMDK","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"GQSC6U27","created_at":"2026-05-18T12:27:06.952714+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/GQSC6U27JKXSEMDKRNFRIYR4WT","json":"https://pith.science/pith/GQSC6U27JKXSEMDKRNFRIYR4WT.json","graph_json":"https://pith.science/api/pith-number/GQSC6U27JKXSEMDKRNFRIYR4WT/graph.json","events_json":"https://pith.science/api/pith-number/GQSC6U27JKXSEMDKRNFRIYR4WT/events.json","paper":"https://pith.science/paper/GQSC6U27"},"agent_actions":{"view_html":"https://pith.science/pith/GQSC6U27JKXSEMDKRNFRIYR4WT","download_json":"https://pith.science/pith/GQSC6U27JKXSEMDKRNFRIYR4WT.json","view_paper":"https://pith.science/paper/GQSC6U27","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.5197&json=true","fetch_graph":"https://pith.science/api/pith-number/GQSC6U27JKXSEMDKRNFRIYR4WT/graph.json","fetch_events":"https://pith.science/api/pith-number/GQSC6U27JKXSEMDKRNFRIYR4WT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GQSC6U27JKXSEMDKRNFRIYR4WT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GQSC6U27JKXSEMDKRNFRIYR4WT/action/storage_attestation","attest_author":"https://pith.science/pith/GQSC6U27JKXSEMDKRNFRIYR4WT/action/author_attestation","sign_citation":"https://pith.science/pith/GQSC6U27JKXSEMDKRNFRIYR4WT/action/citation_signature","submit_replication":"https://pith.science/pith/GQSC6U27JKXSEMDKRNFRIYR4WT/action/replication_record"}},"created_at":"2026-05-18T03:43:39.825140+00:00","updated_at":"2026-05-18T03:43:39.825140+00:00"}