{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KOEADO3R5API2RHPISQFARBRVV","short_pith_number":"pith:KOEADO3R","schema_version":"1.0","canonical_sha256":"538801bb71e81e8d44ef44a0504431ad6dd4544eb243c9e67747113ad3eb1a7a","source":{"kind":"arxiv","id":"1704.06891","version":2},"attestation_state":"computed","paper":{"title":"Higher depth quantum modular forms, multiple Eichler integrals, and $\\frak{sl}_3$ false theta functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.NT","authors_text":"Antun Milas, Jonas Kaszian, Kathrin Bringmann","submitted_at":"2017-04-23T08:07:42Z","abstract_excerpt":"We introduce and study higher depth quantum modular forms. We construct two families of examples coming from rank two false theta functions, whose \"companions\" in the lower half-plane can be also realized both as double Eichler integrals and as non-holomorphic theta series having values of \"double error\" functions as coefficients. In particular, we prove that the false theta of $\\frak{sl}_3$, appearing in the character of the vertex algebra $W^0(p)_{A_2}$, can be written as the sum of two depth two quantum modular forms of positive integral weight."},"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":"1704.06891","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-23T08:07:42Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"12e553beae08bb3213b72f7e11ae7509a16bc9f5d548c4b4405bde0e8e55b688","abstract_canon_sha256":"8088de61d24322138c274f7c1e7f5711940da40d65b75b39d2a0416964c4618e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:52.359752Z","signature_b64":"NR1ZDLzqySmmuq7x1gA6c4P5Nd/VrlM+DVkUKipRfQNcgmAFQYVsBYb2sp4SFKgM79fmFpKYxf92uKndn1+iDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"538801bb71e81e8d44ef44a0504431ad6dd4544eb243c9e67747113ad3eb1a7a","last_reissued_at":"2026-05-18T00:20:52.359344Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:52.359344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher depth quantum modular forms, multiple Eichler integrals, and $\\frak{sl}_3$ false theta functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.NT","authors_text":"Antun Milas, Jonas Kaszian, Kathrin Bringmann","submitted_at":"2017-04-23T08:07:42Z","abstract_excerpt":"We introduce and study higher depth quantum modular forms. We construct two families of examples coming from rank two false theta functions, whose \"companions\" in the lower half-plane can be also realized both as double Eichler integrals and as non-holomorphic theta series having values of \"double error\" functions as coefficients. In particular, we prove that the false theta of $\\frak{sl}_3$, appearing in the character of the vertex algebra $W^0(p)_{A_2}$, can be written as the sum of two depth two quantum modular forms of positive integral weight."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06891","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":"1704.06891","created_at":"2026-05-18T00:20:52.359406+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.06891v2","created_at":"2026-05-18T00:20:52.359406+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06891","created_at":"2026-05-18T00:20:52.359406+00:00"},{"alias_kind":"pith_short_12","alias_value":"KOEADO3R5API","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"KOEADO3R5API2RHP","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"KOEADO3R","created_at":"2026-05-18T12:31:24.725408+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/KOEADO3R5API2RHPISQFARBRVV","json":"https://pith.science/pith/KOEADO3R5API2RHPISQFARBRVV.json","graph_json":"https://pith.science/api/pith-number/KOEADO3R5API2RHPISQFARBRVV/graph.json","events_json":"https://pith.science/api/pith-number/KOEADO3R5API2RHPISQFARBRVV/events.json","paper":"https://pith.science/paper/KOEADO3R"},"agent_actions":{"view_html":"https://pith.science/pith/KOEADO3R5API2RHPISQFARBRVV","download_json":"https://pith.science/pith/KOEADO3R5API2RHPISQFARBRVV.json","view_paper":"https://pith.science/paper/KOEADO3R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.06891&json=true","fetch_graph":"https://pith.science/api/pith-number/KOEADO3R5API2RHPISQFARBRVV/graph.json","fetch_events":"https://pith.science/api/pith-number/KOEADO3R5API2RHPISQFARBRVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KOEADO3R5API2RHPISQFARBRVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KOEADO3R5API2RHPISQFARBRVV/action/storage_attestation","attest_author":"https://pith.science/pith/KOEADO3R5API2RHPISQFARBRVV/action/author_attestation","sign_citation":"https://pith.science/pith/KOEADO3R5API2RHPISQFARBRVV/action/citation_signature","submit_replication":"https://pith.science/pith/KOEADO3R5API2RHPISQFARBRVV/action/replication_record"}},"created_at":"2026-05-18T00:20:52.359406+00:00","updated_at":"2026-05-18T00:20:52.359406+00:00"}