{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4HE63VKZLLWD7MQKVPBJ2LZVAP","short_pith_number":"pith:4HE63VKZ","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"},"canonical_sha256":"e1c9edd5595aec3fb20aabc29d2f3503dafa8474c048aa45076568aaef454127","source":{"kind":"arxiv","id":"1707.00831","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00831","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00831v2","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00831","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"4HE63VKZLLWD","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4HE63VKZLLWD7MQK","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4HE63VKZ","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4HE63VKZLLWD7MQKVPBJ2LZVAP","target":"record","payload":{"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"},"canonical_sha256":"e1c9edd5595aec3fb20aabc29d2f3503dafa8474c048aa45076568aaef454127","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"},"source_kind":"arxiv","source_id":"1707.00831","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I13itcksC587dJOxdJimqChTverJ04Pv0Sh5wzv35m6LQWnBUJkMm2M4Mp2/uGOEV8GNAlVKL4SH5JmhZSl9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T02:38:25.908485Z"},"content_sha256":"d3bb5ea17159504ec852944d00da19fbd23d2f5172a22bf014eed2609e14af0b","schema_version":"1.0","event_id":"sha256:d3bb5ea17159504ec852944d00da19fbd23d2f5172a22bf014eed2609e14af0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4HE63VKZLLWD7MQKVPBJ2LZVAP","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wB8L9Eu0nL4KDuDsEY3RJknZBXocXhUfByaSWcvAuBUEHoWI6EUHhgCDjaluyl5H1jW5AkNfqaBCaB+xODE/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T02:38:25.909314Z"},"content_sha256":"31aeddcf2044da77514ddaa7736968ce5c8ffb8fa4b898f708dc67657b2d5185","schema_version":"1.0","event_id":"sha256:31aeddcf2044da77514ddaa7736968ce5c8ffb8fa4b898f708dc67657b2d5185"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP/bundle.json","state_url":"https://pith.science/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-17T02:38:26Z","links":{"resolver":"https://pith.science/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP","bundle":"https://pith.science/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP/bundle.json","state":"https://pith.science/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4HE63VKZLLWD7MQKVPBJ2LZVAP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4HE63VKZLLWD7MQKVPBJ2LZVAP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c0122730871ee7280388fc616d9e191904abd5873525bd057ab92c27715cc469","cross_cats_sorted":["math-ph","math.MP","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-04T07:03:46Z","title_canon_sha256":"327321d0079e5a9f08ceed5586cf2678895cc418d23e2a0b6de1e0b7b6b1025c"},"schema_version":"1.0","source":{"id":"1707.00831","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00831","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00831v2","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00831","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"4HE63VKZLLWD","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4HE63VKZLLWD7MQK","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4HE63VKZ","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:31aeddcf2044da77514ddaa7736968ce5c8ffb8fa4b898f708dc67657b2d5185","target":"graph","created_at":"2026-05-18T00:22:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Shengmao Zhu","cross_cats":["math-ph","math.MP","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-04T07:03:46Z","title":"Topological strings, quiver varieties and Rogers-Ramanujan identities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00831","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d3bb5ea17159504ec852944d00da19fbd23d2f5172a22bf014eed2609e14af0b","target":"record","created_at":"2026-05-18T00:22:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c0122730871ee7280388fc616d9e191904abd5873525bd057ab92c27715cc469","cross_cats_sorted":["math-ph","math.MP","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-04T07:03:46Z","title_canon_sha256":"327321d0079e5a9f08ceed5586cf2678895cc418d23e2a0b6de1e0b7b6b1025c"},"schema_version":"1.0","source":{"id":"1707.00831","kind":"arxiv","version":2}},"canonical_sha256":"e1c9edd5595aec3fb20aabc29d2f3503dafa8474c048aa45076568aaef454127","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1c9edd5595aec3fb20aabc29d2f3503dafa8474c048aa45076568aaef454127","first_computed_at":"2026-05-18T00:22:06.006056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:06.006056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kx2eBJ97BS9qLQRcOgR/AK6EhhXoD2hdVCCIk3rkGjhwVhQx3CxyFxOMBc73r/3dPjhYkPsgV2A2A2g89NDuAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:06.006581Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.00831","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3bb5ea17159504ec852944d00da19fbd23d2f5172a22bf014eed2609e14af0b","sha256:31aeddcf2044da77514ddaa7736968ce5c8ffb8fa4b898f708dc67657b2d5185"],"state_sha256":"4c23dd9b74c452ae97050b468ef362df480203c06b54be2e75f8436f892063a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oYgQ2NoloacoAKbD4/ETeNNuOSd3mcTl/fvny00iHuk7xYYSZp/ChCF+fh1SyiYCAjQ293ZAbh8qTIldVT6GCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T02:38:26.092944Z","bundle_sha256":"5a078138b32cbf5207c99bc8c9c6bf8209ec96f91b0041284b08fe2859fb17a5"}}