{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:DN77OQOP5VNHWOLMF36GWUOWAR","short_pith_number":"pith:DN77OQOP","schema_version":"1.0","canonical_sha256":"1b7ff741cfed5a7b396c2efc6b51d6047ca663714c0adc85846f09d482f8fd33","source":{"kind":"arxiv","id":"2607.08606","version":1},"attestation_state":"computed","paper":{"title":"Modular Nahm Sums for the Inverse Cartan Matrix of Type $D_r$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Liuquan Wang, Shangwen Wang","submitted_at":"2026-07-09T15:36:04Z","abstract_excerpt":"For $r\\geq 3$ we denote by $\\mathcal{C}(D_r)$ the Cartan matrix of type $D_r$. Recently, Sun and Wang conjectured a Rogers--Ramanujan type identity for the Nahm sum associated with $\\mathcal{C}(D_r)^{-1}$ and the zero vector. They further conjecture that there exist $r-1$ companion modular Nahm sums associated with nonzero vectors. We partially prove this conjecture by constructing $\\lfloor (r+4)/2\\rfloor$ modular Nahm sums for $\\mathcal{C}(D_r)^{-1}$. To prove their modularity, we utilize the method of Bailey pairs to establish various Rogers--Ramanujan type identities. In particular, we conf"},"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":"2607.08606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-09T15:36:04Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"842093670df4c605958be03fddf4642e6c58cd2a79afcfc76c43328e43186e59","abstract_canon_sha256":"ade3b3d9b57718a7891d5fdab239d92bf7e057547a9f3c2b58816484cdc2d35e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-10T01:19:55.065344Z","signature_b64":"Z7FoaDFx0A+Gn4ChjNLziMZRaXm4oEMi1twZPqYENk0Wa3d7cFn2uNqn9+P1htnObzwsRDB6y2sc3jDyU9LuDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b7ff741cfed5a7b396c2efc6b51d6047ca663714c0adc85846f09d482f8fd33","last_reissued_at":"2026-07-10T01:19:55.064722Z","signature_status":"signed_v1","first_computed_at":"2026-07-10T01:19:55.064722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modular Nahm Sums for the Inverse Cartan Matrix of Type $D_r$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Liuquan Wang, Shangwen Wang","submitted_at":"2026-07-09T15:36:04Z","abstract_excerpt":"For $r\\geq 3$ we denote by $\\mathcal{C}(D_r)$ the Cartan matrix of type $D_r$. Recently, Sun and Wang conjectured a Rogers--Ramanujan type identity for the Nahm sum associated with $\\mathcal{C}(D_r)^{-1}$ and the zero vector. They further conjecture that there exist $r-1$ companion modular Nahm sums associated with nonzero vectors. We partially prove this conjecture by constructing $\\lfloor (r+4)/2\\rfloor$ modular Nahm sums for $\\mathcal{C}(D_r)^{-1}$. To prove their modularity, we utilize the method of Bailey pairs to establish various Rogers--Ramanujan type identities. In particular, we conf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08606","kind":"arxiv","version":1},"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/2607.08606/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":"2607.08606","created_at":"2026-07-10T01:19:55.064846+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.08606v1","created_at":"2026-07-10T01:19:55.064846+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08606","created_at":"2026-07-10T01:19:55.064846+00:00"},{"alias_kind":"pith_short_12","alias_value":"DN77OQOP5VNH","created_at":"2026-07-10T01:19:55.064846+00:00"},{"alias_kind":"pith_short_16","alias_value":"DN77OQOP5VNHWOLM","created_at":"2026-07-10T01:19:55.064846+00:00"},{"alias_kind":"pith_short_8","alias_value":"DN77OQOP","created_at":"2026-07-10T01:19:55.064846+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/DN77OQOP5VNHWOLMF36GWUOWAR","json":"https://pith.science/pith/DN77OQOP5VNHWOLMF36GWUOWAR.json","graph_json":"https://pith.science/api/pith-number/DN77OQOP5VNHWOLMF36GWUOWAR/graph.json","events_json":"https://pith.science/api/pith-number/DN77OQOP5VNHWOLMF36GWUOWAR/events.json","paper":"https://pith.science/paper/DN77OQOP"},"agent_actions":{"view_html":"https://pith.science/pith/DN77OQOP5VNHWOLMF36GWUOWAR","download_json":"https://pith.science/pith/DN77OQOP5VNHWOLMF36GWUOWAR.json","view_paper":"https://pith.science/paper/DN77OQOP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.08606&json=true","fetch_graph":"https://pith.science/api/pith-number/DN77OQOP5VNHWOLMF36GWUOWAR/graph.json","fetch_events":"https://pith.science/api/pith-number/DN77OQOP5VNHWOLMF36GWUOWAR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DN77OQOP5VNHWOLMF36GWUOWAR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DN77OQOP5VNHWOLMF36GWUOWAR/action/storage_attestation","attest_author":"https://pith.science/pith/DN77OQOP5VNHWOLMF36GWUOWAR/action/author_attestation","sign_citation":"https://pith.science/pith/DN77OQOP5VNHWOLMF36GWUOWAR/action/citation_signature","submit_replication":"https://pith.science/pith/DN77OQOP5VNHWOLMF36GWUOWAR/action/replication_record"}},"created_at":"2026-07-10T01:19:55.064846+00:00","updated_at":"2026-07-10T01:19:55.064846+00:00"}