{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GQSC6U27JKXSEMDKRNFRIYR4WT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ed7990cbfbf40f540237fd34fb33da3ce02f6eacc5030b0caed8a955b15171f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-24T08:57:55Z","title_canon_sha256":"eb3f8e71fb20bee1a8207aaf1623961c4618377a41f0a4d7f431bb5116ea8c00"},"schema_version":"1.0","source":{"id":"1209.5197","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5197","created_at":"2026-05-18T03:43:39Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5197v2","created_at":"2026-05-18T03:43:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5197","created_at":"2026-05-18T03:43:39Z"},{"alias_kind":"pith_short_12","alias_value":"GQSC6U27JKXS","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GQSC6U27JKXSEMDK","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GQSC6U27","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:e59f50e7a4a8530a042535e8f92aed3ee04fe4be94c6d7fa4eb5b0aa7ee10820","target":"graph","created_at":"2026-05-18T03:43:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Claudia Alfes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-24T08:57:55Z","title":"Formulas for the coefficients of half-integral weight harmonic Maass forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5197","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3ef8cc9c7f37f7a65e99dbdc3c24b552431fce4a9d45eb8794bc1841f3acc8e0","target":"record","created_at":"2026-05-18T03:43:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ed7990cbfbf40f540237fd34fb33da3ce02f6eacc5030b0caed8a955b15171f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-24T08:57:55Z","title_canon_sha256":"eb3f8e71fb20bee1a8207aaf1623961c4618377a41f0a4d7f431bb5116ea8c00"},"schema_version":"1.0","source":{"id":"1209.5197","kind":"arxiv","version":2}},"canonical_sha256":"34242f535f4aaf22306a8b4b14623cb4e1f127c71c2cd129745f5fd5dc0306f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34242f535f4aaf22306a8b4b14623cb4e1f127c71c2cd129745f5fd5dc0306f2","first_computed_at":"2026-05-18T03:43:39.825045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:39.825045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PfIaQGn5M+kkTG5WuPMeFxwXX0DbbpNXnuZ8avAzc5lLgvdHUNFzJ7WTJBeqfqRZl8EYxjm3ucsQLdvi9ClpAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:39.825684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.5197","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ef8cc9c7f37f7a65e99dbdc3c24b552431fce4a9d45eb8794bc1841f3acc8e0","sha256:e59f50e7a4a8530a042535e8f92aed3ee04fe4be94c6d7fa4eb5b0aa7ee10820"],"state_sha256":"9bd2755d52cfc4aed2396d79acdbe74fe7f7e0b9b9cb1fc8d25bfd0af85f49ae"}