{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:4KBDABK63CTR5MU4VZVMX3F7VP","short_pith_number":"pith:4KBDABK6","schema_version":"1.0","canonical_sha256":"e28230055ed8a71eb29cae6acbecbfabe80eeeb6e7a91af0302a85ee7131c63c","source":{"kind":"arxiv","id":"2502.19309","version":1},"attestation_state":"computed","paper":{"title":"Rogers--Ramanujan Type Identities for Rank Two Partial Nahm Sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Liuquan Wang, Wentao Zeng","submitted_at":"2025-02-26T17:07:19Z","abstract_excerpt":"Let $A$ be a $r\\times r$ rational nonzero symmetric matrix, $B$ a rational column vector, $C$ a rational scalar. For any integer lattice $L$ and vector $v$ of $\\mathbb{Z}^r$, we define Nahm sum on the lattice coset $v+L\\in \\mathbb{Z}^r/L$: \\begin{align*}\\label{eq-lattice-sum} f_{A,B,C,v+L}(q):=\\sum_{n=(n_1,\\dots,n_r)^\\mathrm{T} \\in v+L} \\frac{q^{\\frac{1}{2}n^\\mathrm{T} An+n^\\mathrm{T} B+C}}{(q;q)_{n_1}\\cdots (q;q)_{n_r}}. \\end{align*} If $L$ is a full rank lattice and a proper subset of $\\mathbb{Z}^r$, then we call $f_{A,B,C,v+L}(q)$ a rank $r$ partial Nahm sum. When the rank $r=1$, we find ei"},"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":"2502.19309","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-02-26T17:07:19Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"83209672ef8d1536d92b4fd3938b0c4cad2392e2a909d01d2d840dd481db9cca","abstract_canon_sha256":"7d23502e3f2f1cab182b89686245c5f2c00a478da7d966c02659be0b300a2fb9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:20:29.840190Z","signature_b64":"L4gFFFAZIMDsv0CZtdkY//jd/R+vqfa7fJFDLFQX725aqhA6/2YMTpH56CqrZf9Llr62TTAub/E5XzvHIUjuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e28230055ed8a71eb29cae6acbecbfabe80eeeb6e7a91af0302a85ee7131c63c","last_reissued_at":"2026-07-05T10:20:29.839711Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:20:29.839711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rogers--Ramanujan Type Identities for Rank Two Partial Nahm Sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Liuquan Wang, Wentao Zeng","submitted_at":"2025-02-26T17:07:19Z","abstract_excerpt":"Let $A$ be a $r\\times r$ rational nonzero symmetric matrix, $B$ a rational column vector, $C$ a rational scalar. For any integer lattice $L$ and vector $v$ of $\\mathbb{Z}^r$, we define Nahm sum on the lattice coset $v+L\\in \\mathbb{Z}^r/L$: \\begin{align*}\\label{eq-lattice-sum} f_{A,B,C,v+L}(q):=\\sum_{n=(n_1,\\dots,n_r)^\\mathrm{T} \\in v+L} \\frac{q^{\\frac{1}{2}n^\\mathrm{T} An+n^\\mathrm{T} B+C}}{(q;q)_{n_1}\\cdots (q;q)_{n_r}}. \\end{align*} If $L$ is a full rank lattice and a proper subset of $\\mathbb{Z}^r$, then we call $f_{A,B,C,v+L}(q)$ a rank $r$ partial Nahm sum. When the rank $r=1$, we find ei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.19309","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/2502.19309/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":"2502.19309","created_at":"2026-07-05T10:20:29.839770+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.19309v1","created_at":"2026-07-05T10:20:29.839770+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.19309","created_at":"2026-07-05T10:20:29.839770+00:00"},{"alias_kind":"pith_short_12","alias_value":"4KBDABK63CTR","created_at":"2026-07-05T10:20:29.839770+00:00"},{"alias_kind":"pith_short_16","alias_value":"4KBDABK63CTR5MU4","created_at":"2026-07-05T10:20:29.839770+00:00"},{"alias_kind":"pith_short_8","alias_value":"4KBDABK6","created_at":"2026-07-05T10:20:29.839770+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/4KBDABK63CTR5MU4VZVMX3F7VP","json":"https://pith.science/pith/4KBDABK63CTR5MU4VZVMX3F7VP.json","graph_json":"https://pith.science/api/pith-number/4KBDABK63CTR5MU4VZVMX3F7VP/graph.json","events_json":"https://pith.science/api/pith-number/4KBDABK63CTR5MU4VZVMX3F7VP/events.json","paper":"https://pith.science/paper/4KBDABK6"},"agent_actions":{"view_html":"https://pith.science/pith/4KBDABK63CTR5MU4VZVMX3F7VP","download_json":"https://pith.science/pith/4KBDABK63CTR5MU4VZVMX3F7VP.json","view_paper":"https://pith.science/paper/4KBDABK6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.19309&json=true","fetch_graph":"https://pith.science/api/pith-number/4KBDABK63CTR5MU4VZVMX3F7VP/graph.json","fetch_events":"https://pith.science/api/pith-number/4KBDABK63CTR5MU4VZVMX3F7VP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4KBDABK63CTR5MU4VZVMX3F7VP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4KBDABK63CTR5MU4VZVMX3F7VP/action/storage_attestation","attest_author":"https://pith.science/pith/4KBDABK63CTR5MU4VZVMX3F7VP/action/author_attestation","sign_citation":"https://pith.science/pith/4KBDABK63CTR5MU4VZVMX3F7VP/action/citation_signature","submit_replication":"https://pith.science/pith/4KBDABK63CTR5MU4VZVMX3F7VP/action/replication_record"}},"created_at":"2026-07-05T10:20:29.839770+00:00","updated_at":"2026-07-05T10:20:29.839770+00:00"}