{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5ZFICZAP6DC4ALVAG4X5ROVE6C","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":"46dc81780f4681c0883676b76ac28d8634a125187601448a2773ebae24a487b8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-04-06T20:04:56Z","title_canon_sha256":"0c2ce407b9b3bf2f2b4d146e3fb8d9a3d2e9ea128a8582239b13db62bee00f54"},"schema_version":"1.0","source":{"id":"1104.1182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1182","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1182v1","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1182","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"pith_short_12","alias_value":"5ZFICZAP6DC4","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"5ZFICZAP6DC4ALVA","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"5ZFICZAP","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:15c8956c16c4c3ff5a3c8d1ecb9e24276e564cdca3db4935aa2d09e70528c7b7","target":"graph","created_at":"2026-05-18T04:24:52Z","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":"We prove that the coefficients of certain weight -1/2 harmonic Maass forms are traces of singular moduli for weak Maass forms. To prove this theorem, we construct a theta lift from spaces of weight -2 harmonic weak Maass forms to spaces of weight -1/2 vector-valued harmonic weak Maass forms on Mp_2(Z), a result which is of independent interest. We then prove a general theorem which guarantees (with bounded denominator) when such Maass singular moduli are algebraic. As an example of these results, we derive a formula for the partition function p(n) as a finite sum of algebraic numbers which lie","authors_text":"Jan Hendrik Bruinier, Ken Ono","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-04-06T20:04:56Z","title":"Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1182","kind":"arxiv","version":1},"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":"sha256:16a0c64daf83fcd8c4d63164f682a56d54df61e0335b3aab9c8363f2072081b2","target":"record","created_at":"2026-05-18T04:24:52Z","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":"46dc81780f4681c0883676b76ac28d8634a125187601448a2773ebae24a487b8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-04-06T20:04:56Z","title_canon_sha256":"0c2ce407b9b3bf2f2b4d146e3fb8d9a3d2e9ea128a8582239b13db62bee00f54"},"schema_version":"1.0","source":{"id":"1104.1182","kind":"arxiv","version":1}},"canonical_sha256":"ee4a81640ff0c5c02ea0372fd8baa4f083fef0b578f683c7129f5114b00636fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee4a81640ff0c5c02ea0372fd8baa4f083fef0b578f683c7129f5114b00636fc","first_computed_at":"2026-05-18T04:24:52.668064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:52.668064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fl3CJU9dsENyag5WdowJPgJ1wUU4dj0WPHJI44S4LcpfMU7rkof1bfFvlD6QgSAWbBAPFrRoIx5J0fwIrY0pDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:52.668525Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16a0c64daf83fcd8c4d63164f682a56d54df61e0335b3aab9c8363f2072081b2","sha256:15c8956c16c4c3ff5a3c8d1ecb9e24276e564cdca3db4935aa2d09e70528c7b7"],"state_sha256":"e1b7974057bde4a7e50270f7d5b6dc42c639df69eca661dcb4358827ef5e01cf"}