{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ESKWG4TIFQOOTUE42ADQVNKQ76","short_pith_number":"pith:ESKWG4TI","schema_version":"1.0","canonical_sha256":"24956372682c1ce9d09cd0070ab550ff9a9176f6ab0035c60b3b62d0e192f53d","source":{"kind":"arxiv","id":"2502.06449","version":2},"attestation_state":"computed","paper":{"title":"Denominator identity for the affine Lie superalgebra $\\widehat{\\mathfrak{spo}}(2m,2m+1)$ and indefinite theta functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Miyu Suzuki, Toshiki Matsusaka","submitted_at":"2025-02-10T13:26:37Z","abstract_excerpt":"In 1994, Kac and Wakimoto found the denominator identity for classical affine Lie superalgebras, generalizing that for affine Lie algebras. As an application, they obtained power series identities for some powers of $\\triangle(q)$, where $\\triangle(q)$ is the generating function of triangular numbers. In this article, we give a different proof of one of their identities. The main step is to prove that a certain indefinite theta function involving spherical polynomials is a modular form. We use the technique recently developed by Roehrig and Zwegers."},"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":"2502.06449","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-02-10T13:26:37Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3d63d29d9fc9fe10c8a0391bee886a913cc48ad5e21e9b44a3a636a3fc75d5b3","abstract_canon_sha256":"98725896b8d9eb376f26ab53216406cc306243d5d6baa4b60c67982cd1545181"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:27.932222Z","signature_b64":"BEVNfhXiaH0zLmYuqk8Q8BP6SRNpy4Od2woIjeMImociuZnMQmy5XTc2Wz502cpyl3WznzQZHBfA/h24kGupAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24956372682c1ce9d09cd0070ab550ff9a9176f6ab0035c60b3b62d0e192f53d","last_reissued_at":"2026-07-05T11:36:27.931788Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:27.931788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Denominator identity for the affine Lie superalgebra $\\widehat{\\mathfrak{spo}}(2m,2m+1)$ and indefinite theta functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Miyu Suzuki, Toshiki Matsusaka","submitted_at":"2025-02-10T13:26:37Z","abstract_excerpt":"In 1994, Kac and Wakimoto found the denominator identity for classical affine Lie superalgebras, generalizing that for affine Lie algebras. As an application, they obtained power series identities for some powers of $\\triangle(q)$, where $\\triangle(q)$ is the generating function of triangular numbers. In this article, we give a different proof of one of their identities. The main step is to prove that a certain indefinite theta function involving spherical polynomials is a modular form. We use the technique recently developed by Roehrig and Zwegers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06449","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.06449/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2502.06449","created_at":"2026-07-05T11:36:27.931844+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.06449v2","created_at":"2026-07-05T11:36:27.931844+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06449","created_at":"2026-07-05T11:36:27.931844+00:00"},{"alias_kind":"pith_short_12","alias_value":"ESKWG4TIFQOO","created_at":"2026-07-05T11:36:27.931844+00:00"},{"alias_kind":"pith_short_16","alias_value":"ESKWG4TIFQOOTUE4","created_at":"2026-07-05T11:36:27.931844+00:00"},{"alias_kind":"pith_short_8","alias_value":"ESKWG4TI","created_at":"2026-07-05T11:36:27.931844+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.04722","citing_title":"Indefinite theta functions arising from affine Lie superalgebras and sums of triangular numbers","ref_index":7,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ESKWG4TIFQOOTUE42ADQVNKQ76","json":"https://pith.science/pith/ESKWG4TIFQOOTUE42ADQVNKQ76.json","graph_json":"https://pith.science/api/pith-number/ESKWG4TIFQOOTUE42ADQVNKQ76/graph.json","events_json":"https://pith.science/api/pith-number/ESKWG4TIFQOOTUE42ADQVNKQ76/events.json","paper":"https://pith.science/paper/ESKWG4TI"},"agent_actions":{"view_html":"https://pith.science/pith/ESKWG4TIFQOOTUE42ADQVNKQ76","download_json":"https://pith.science/pith/ESKWG4TIFQOOTUE42ADQVNKQ76.json","view_paper":"https://pith.science/paper/ESKWG4TI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.06449&json=true","fetch_graph":"https://pith.science/api/pith-number/ESKWG4TIFQOOTUE42ADQVNKQ76/graph.json","fetch_events":"https://pith.science/api/pith-number/ESKWG4TIFQOOTUE42ADQVNKQ76/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ESKWG4TIFQOOTUE42ADQVNKQ76/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ESKWG4TIFQOOTUE42ADQVNKQ76/action/storage_attestation","attest_author":"https://pith.science/pith/ESKWG4TIFQOOTUE42ADQVNKQ76/action/author_attestation","sign_citation":"https://pith.science/pith/ESKWG4TIFQOOTUE42ADQVNKQ76/action/citation_signature","submit_replication":"https://pith.science/pith/ESKWG4TIFQOOTUE42ADQVNKQ76/action/replication_record"}},"created_at":"2026-07-05T11:36:27.931844+00:00","updated_at":"2026-07-05T11:36:27.931844+00:00"}