{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:M7Q3DMFQABY2OEECEIJITZ5QJF","short_pith_number":"pith:M7Q3DMFQ","schema_version":"1.0","canonical_sha256":"67e1b1b0b00071a71082221289e7b0495444a66de4217f5e1f823477bf09c1b5","source":{"kind":"arxiv","id":"2108.06995","version":2},"attestation_state":"computed","paper":{"title":"Topological recursion and uncoupled BPS structures II: Voros symbols and the $\\tau$-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG","math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Kohei Iwaki, Omar Kidwai","submitted_at":"2021-08-16T09:57:49Z","abstract_excerpt":"We continue our study of the correspondence between BPS structures and topological recursion in the uncoupled case, this time from the viewpoint of quantum curves. For spectral curves of hypergeometric type, we show the Borel-resummed Voros symbols of the corresponding quantum curves solve Bridgeland's \"BPS Riemann-Hilbert problem\". In particular, they satisfy the required jump property in agreement with the generalized definition of BPS indices $\\Omega$ in our previous work. Furthermore, we observe the Voros coefficients define a closed one-form on the parameter space, and show that (log of) "},"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":"2108.06995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-08-16T09:57:49Z","cross_cats_sorted":["hep-th","math.AG","math.CA","math.MP"],"title_canon_sha256":"87e7c77bb0bfaf641615152aa7caccefd663c50ea5f949893e0b06a98bd0fbcd","abstract_canon_sha256":"a162749b0356cb29ccd9e71076ff657c43170b448b9945eaad0511862e82580f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:49:09.113760Z","signature_b64":"grFMbvnY2vd0+EanTKyiq91ZE2z64FYeO7R8mTjO33lSwU4A4hxWUKKNMOsmT5IUpbwiUVS/anQjsO82uwGsBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67e1b1b0b00071a71082221289e7b0495444a66de4217f5e1f823477bf09c1b5","last_reissued_at":"2026-07-05T07:49:09.113234Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:49:09.113234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological recursion and uncoupled BPS structures II: Voros symbols and the $\\tau$-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG","math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Kohei Iwaki, Omar Kidwai","submitted_at":"2021-08-16T09:57:49Z","abstract_excerpt":"We continue our study of the correspondence between BPS structures and topological recursion in the uncoupled case, this time from the viewpoint of quantum curves. For spectral curves of hypergeometric type, we show the Borel-resummed Voros symbols of the corresponding quantum curves solve Bridgeland's \"BPS Riemann-Hilbert problem\". In particular, they satisfy the required jump property in agreement with the generalized definition of BPS indices $\\Omega$ in our previous work. Furthermore, we observe the Voros coefficients define a closed one-form on the parameter space, and show that (log of) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.06995","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/2108.06995/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":"2108.06995","created_at":"2026-07-05T07:49:09.113294+00:00"},{"alias_kind":"arxiv_version","alias_value":"2108.06995v2","created_at":"2026-07-05T07:49:09.113294+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.06995","created_at":"2026-07-05T07:49:09.113294+00:00"},{"alias_kind":"pith_short_12","alias_value":"M7Q3DMFQABY2","created_at":"2026-07-05T07:49:09.113294+00:00"},{"alias_kind":"pith_short_16","alias_value":"M7Q3DMFQABY2OEEC","created_at":"2026-07-05T07:49:09.113294+00:00"},{"alias_kind":"pith_short_8","alias_value":"M7Q3DMFQ","created_at":"2026-07-05T07:49:09.113294+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2512.17599","citing_title":"Les Houches Lectures on Exact WKB Analysis and Painlev\\'e Equations","ref_index":93,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M7Q3DMFQABY2OEECEIJITZ5QJF","json":"https://pith.science/pith/M7Q3DMFQABY2OEECEIJITZ5QJF.json","graph_json":"https://pith.science/api/pith-number/M7Q3DMFQABY2OEECEIJITZ5QJF/graph.json","events_json":"https://pith.science/api/pith-number/M7Q3DMFQABY2OEECEIJITZ5QJF/events.json","paper":"https://pith.science/paper/M7Q3DMFQ"},"agent_actions":{"view_html":"https://pith.science/pith/M7Q3DMFQABY2OEECEIJITZ5QJF","download_json":"https://pith.science/pith/M7Q3DMFQABY2OEECEIJITZ5QJF.json","view_paper":"https://pith.science/paper/M7Q3DMFQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2108.06995&json=true","fetch_graph":"https://pith.science/api/pith-number/M7Q3DMFQABY2OEECEIJITZ5QJF/graph.json","fetch_events":"https://pith.science/api/pith-number/M7Q3DMFQABY2OEECEIJITZ5QJF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M7Q3DMFQABY2OEECEIJITZ5QJF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M7Q3DMFQABY2OEECEIJITZ5QJF/action/storage_attestation","attest_author":"https://pith.science/pith/M7Q3DMFQABY2OEECEIJITZ5QJF/action/author_attestation","sign_citation":"https://pith.science/pith/M7Q3DMFQABY2OEECEIJITZ5QJF/action/citation_signature","submit_replication":"https://pith.science/pith/M7Q3DMFQABY2OEECEIJITZ5QJF/action/replication_record"}},"created_at":"2026-07-05T07:49:09.113294+00:00","updated_at":"2026-07-05T07:49:09.113294+00:00"}