{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4HE63VKZLLWD7MQKVPBJ2LZVAP","short_pith_number":"pith:4HE63VKZ","schema_version":"1.0","canonical_sha256":"e1c9edd5595aec3fb20aabc29d2f3503dafa8474c048aa45076568aaef454127","source":{"kind":"arxiv","id":"1707.00831","version":2},"attestation_state":"computed","paper":{"title":"Topological strings, quiver varieties and Rogers-Ramanujan identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NT"],"primary_cat":"math.AG","authors_text":"Shengmao Zhu","submitted_at":"2017-07-04T07:03:46Z","abstract_excerpt":"Motivated by some recent works on BPS invariants of open strings/knot invariants, we guess there may be a general correspondence between the Ooguri-Vafa invariants of toric Calabi-Yau 3-folds and cohomologies of Nakajima quiver varieties. In this short note, we provide a toy model to explain this correspondence. More precisely, we study the topological open string model of $\\mathbb{C}^3$ with one Aganagic-Vafa brane $\\mathcal{D}_\\tau$, and we show that, when $\\tau\\leq 0$, its Ooguri-Vafa invariants are given by the Betti numbers of certain quiver variety. Moreover, the existence of Ooguri-Vafa"},"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":"1707.00831","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-04T07:03:46Z","cross_cats_sorted":["math-ph","math.MP","math.NT"],"title_canon_sha256":"327321d0079e5a9f08ceed5586cf2678895cc418d23e2a0b6de1e0b7b6b1025c","abstract_canon_sha256":"c0122730871ee7280388fc616d9e191904abd5873525bd057ab92c27715cc469"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:06.006581Z","signature_b64":"kx2eBJ97BS9qLQRcOgR/AK6EhhXoD2hdVCCIk3rkGjhwVhQx3CxyFxOMBc73r/3dPjhYkPsgV2A2A2g89NDuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1c9edd5595aec3fb20aabc29d2f3503dafa8474c048aa45076568aaef454127","last_reissued_at":"2026-05-18T00:22:06.006056Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:06.006056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological strings, quiver varieties and Rogers-Ramanujan identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NT"],"primary_cat":"math.AG","authors_text":"Shengmao Zhu","submitted_at":"2017-07-04T07:03:46Z","abstract_excerpt":"Motivated by some recent works on BPS invariants of open strings/knot invariants, we guess there may be a general correspondence between the Ooguri-Vafa invariants of toric Calabi-Yau 3-folds and cohomologies of Nakajima quiver varieties. In this short note, we provide a toy model to explain this correspondence. More precisely, we study the topological open string model of $\\mathbb{C}^3$ with one Aganagic-Vafa brane $\\mathcal{D}_\\tau$, and we show that, when $\\tau\\leq 0$, its Ooguri-Vafa invariants are given by the Betti numbers of certain quiver variety. Moreover, the existence of Ooguri-Vafa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00831","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":"1707.00831","created_at":"2026-05-18T00:22:06.006146+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.00831v2","created_at":"2026-05-18T00:22:06.006146+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00831","created_at":"2026-05-18T00:22:06.006146+00:00"},{"alias_kind":"pith_short_12","alias_value":"4HE63VKZLLWD","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"4HE63VKZLLWD7MQK","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"4HE63VKZ","created_at":"2026-05-18T12:30:58.224056+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.02059","citing_title":"A survey of knots and quivers","ref_index":39,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP","json":"https://pith.science/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP.json","graph_json":"https://pith.science/api/pith-number/4HE63VKZLLWD7MQKVPBJ2LZVAP/graph.json","events_json":"https://pith.science/api/pith-number/4HE63VKZLLWD7MQKVPBJ2LZVAP/events.json","paper":"https://pith.science/paper/4HE63VKZ"},"agent_actions":{"view_html":"https://pith.science/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP","download_json":"https://pith.science/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP.json","view_paper":"https://pith.science/paper/4HE63VKZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.00831&json=true","fetch_graph":"https://pith.science/api/pith-number/4HE63VKZLLWD7MQKVPBJ2LZVAP/graph.json","fetch_events":"https://pith.science/api/pith-number/4HE63VKZLLWD7MQKVPBJ2LZVAP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP/action/storage_attestation","attest_author":"https://pith.science/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP/action/author_attestation","sign_citation":"https://pith.science/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP/action/citation_signature","submit_replication":"https://pith.science/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP/action/replication_record"}},"created_at":"2026-05-18T00:22:06.006146+00:00","updated_at":"2026-05-18T00:22:06.006146+00:00"}