{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BXLEBT4ISA6EZTS6W7DALXK2FQ","short_pith_number":"pith:BXLEBT4I","schema_version":"1.0","canonical_sha256":"0dd640cf88903c4cce5eb7c605dd5a2c302c12aed01b20ab657e7cc18db562ca","source":{"kind":"arxiv","id":"1207.5600","version":2},"attestation_state":"computed","paper":{"title":"Harmonic Maass-Jacobi forms with singularities and a theta-like decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kathrin Bringmann, Martin Raum, Olav Richter","submitted_at":"2012-07-24T07:03:24Z","abstract_excerpt":"Real-analytic Jacobi forms play key roles in different areas of mathematics and physics, but a satisfactory theory of such Jacobi forms has been lacking. In this paper, we fill this gap by introducing a space of harmonic Maass-Jacobi forms with singularities which includes the real-analytic Jacobi forms from Zwegers's PhD thesis. We provide several structure results for the space of such Jacobi forms, and we employ Zwegers's $\\widehat\\mu$-functions to establish a theta-like decomposition."},"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":"1207.5600","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-24T07:03:24Z","cross_cats_sorted":[],"title_canon_sha256":"ba568f0b8e523af26cc73d38a43c18d7dda7df23818a0ca707743d666c5aa656","abstract_canon_sha256":"ed22ec1f885582f788ad7cc30615bf029d0768e4e0580f90676f916423d53351"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:48.642423Z","signature_b64":"f48A79fBIIR2gErXOyE8RrCC970to4YyQUYMonaX6eZM6hMHBAfSnyTv7GaI6QlN5Y6fnsoAsNt1/WPf9dfVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0dd640cf88903c4cce5eb7c605dd5a2c302c12aed01b20ab657e7cc18db562ca","last_reissued_at":"2026-05-18T02:55:48.641777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:48.641777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Harmonic Maass-Jacobi forms with singularities and a theta-like decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kathrin Bringmann, Martin Raum, Olav Richter","submitted_at":"2012-07-24T07:03:24Z","abstract_excerpt":"Real-analytic Jacobi forms play key roles in different areas of mathematics and physics, but a satisfactory theory of such Jacobi forms has been lacking. In this paper, we fill this gap by introducing a space of harmonic Maass-Jacobi forms with singularities which includes the real-analytic Jacobi forms from Zwegers's PhD thesis. We provide several structure results for the space of such Jacobi forms, and we employ Zwegers's $\\widehat\\mu$-functions to establish a theta-like decomposition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5600","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":"1207.5600","created_at":"2026-05-18T02:55:48.641883+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.5600v2","created_at":"2026-05-18T02:55:48.641883+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5600","created_at":"2026-05-18T02:55:48.641883+00:00"},{"alias_kind":"pith_short_12","alias_value":"BXLEBT4ISA6E","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"BXLEBT4ISA6EZTS6","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"BXLEBT4I","created_at":"2026-05-18T12:27:01.376967+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/BXLEBT4ISA6EZTS6W7DALXK2FQ","json":"https://pith.science/pith/BXLEBT4ISA6EZTS6W7DALXK2FQ.json","graph_json":"https://pith.science/api/pith-number/BXLEBT4ISA6EZTS6W7DALXK2FQ/graph.json","events_json":"https://pith.science/api/pith-number/BXLEBT4ISA6EZTS6W7DALXK2FQ/events.json","paper":"https://pith.science/paper/BXLEBT4I"},"agent_actions":{"view_html":"https://pith.science/pith/BXLEBT4ISA6EZTS6W7DALXK2FQ","download_json":"https://pith.science/pith/BXLEBT4ISA6EZTS6W7DALXK2FQ.json","view_paper":"https://pith.science/paper/BXLEBT4I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.5600&json=true","fetch_graph":"https://pith.science/api/pith-number/BXLEBT4ISA6EZTS6W7DALXK2FQ/graph.json","fetch_events":"https://pith.science/api/pith-number/BXLEBT4ISA6EZTS6W7DALXK2FQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BXLEBT4ISA6EZTS6W7DALXK2FQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BXLEBT4ISA6EZTS6W7DALXK2FQ/action/storage_attestation","attest_author":"https://pith.science/pith/BXLEBT4ISA6EZTS6W7DALXK2FQ/action/author_attestation","sign_citation":"https://pith.science/pith/BXLEBT4ISA6EZTS6W7DALXK2FQ/action/citation_signature","submit_replication":"https://pith.science/pith/BXLEBT4ISA6EZTS6W7DALXK2FQ/action/replication_record"}},"created_at":"2026-05-18T02:55:48.641883+00:00","updated_at":"2026-05-18T02:55:48.641883+00:00"}