{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:U6CEVRAKP6ASL64EEXXU2FOVVU","short_pith_number":"pith:U6CEVRAK","schema_version":"1.0","canonical_sha256":"a7844ac40a7f8125fb8425ef4d15d5ad1c631170b4521995614d91891c4ed5a9","source":{"kind":"arxiv","id":"1401.7094","version":4},"attestation_state":"computed","paper":{"title":"Exact WKB analysis and cluster algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.CA","authors_text":"Kohei Iwaki, Tomoki Nakanishi","submitted_at":"2014-01-28T06:31:06Z","abstract_excerpt":"We develop the mutation theory in the exact WKB analysis using the framework of cluster algebras. Under a continuous deformation of the potential of the Schr\\\"odinger equation on a compact Riemann surface, the Stokes graph may change the topology. We call this phenomenon the mutation of Stokes graphs. Along the mutation of Stokes graphs, the Voros symbols, which are monodromy data of the equation, also mutate due to the Stokes phenomenon. We show that the Voros symbols mutate as variables of a cluster algebra with surface realization. As an application, we obtain the identities of Stokes autom"},"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":"1401.7094","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-01-28T06:31:06Z","cross_cats_sorted":["math.QA","math.RA"],"title_canon_sha256":"8626ff6106114836706384e2d4a62b37d8f20250f8fba004d846d08d49e22c4d","abstract_canon_sha256":"c5ef137d7fa8d20105902658da506c09714eb0503b53a623b437dacfbe9e41a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:44.673478Z","signature_b64":"ugq0LEUrRmz9Cb8kwKq1Ytt2XfX+Qgdn2rvZRdnUQxpLogbrWam+OC0FlQIlireHpzxOEMz0H1sjvclVED/IBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7844ac40a7f8125fb8425ef4d15d5ad1c631170b4521995614d91891c4ed5a9","last_reissued_at":"2026-05-18T02:37:44.673022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:44.673022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact WKB analysis and cluster algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.CA","authors_text":"Kohei Iwaki, Tomoki Nakanishi","submitted_at":"2014-01-28T06:31:06Z","abstract_excerpt":"We develop the mutation theory in the exact WKB analysis using the framework of cluster algebras. Under a continuous deformation of the potential of the Schr\\\"odinger equation on a compact Riemann surface, the Stokes graph may change the topology. We call this phenomenon the mutation of Stokes graphs. Along the mutation of Stokes graphs, the Voros symbols, which are monodromy data of the equation, also mutate due to the Stokes phenomenon. We show that the Voros symbols mutate as variables of a cluster algebra with surface realization. As an application, we obtain the identities of Stokes autom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7094","kind":"arxiv","version":4},"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":"1401.7094","created_at":"2026-05-18T02:37:44.673085+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.7094v4","created_at":"2026-05-18T02:37:44.673085+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7094","created_at":"2026-05-18T02:37:44.673085+00:00"},{"alias_kind":"pith_short_12","alias_value":"U6CEVRAKP6AS","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"U6CEVRAKP6ASL64E","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"U6CEVRAK","created_at":"2026-05-18T12:28:52.271510+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2512.17599","citing_title":"Les Houches Lectures on Exact WKB Analysis and Painlev\\'e Equations","ref_index":99,"is_internal_anchor":true},{"citing_arxiv_id":"2510.11766","citing_title":"Exact WKB method for radial Schr\\\"odinger equation","ref_index":3,"is_internal_anchor":true},{"citing_arxiv_id":"2605.03887","citing_title":"Classical correlation functions at strong coupling from hexagonalization","ref_index":57,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06079","citing_title":"Accessory Parameter of Confluent Heun Equations, Voros Periods and classical irregular conformal blocks","ref_index":23,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U6CEVRAKP6ASL64EEXXU2FOVVU","json":"https://pith.science/pith/U6CEVRAKP6ASL64EEXXU2FOVVU.json","graph_json":"https://pith.science/api/pith-number/U6CEVRAKP6ASL64EEXXU2FOVVU/graph.json","events_json":"https://pith.science/api/pith-number/U6CEVRAKP6ASL64EEXXU2FOVVU/events.json","paper":"https://pith.science/paper/U6CEVRAK"},"agent_actions":{"view_html":"https://pith.science/pith/U6CEVRAKP6ASL64EEXXU2FOVVU","download_json":"https://pith.science/pith/U6CEVRAKP6ASL64EEXXU2FOVVU.json","view_paper":"https://pith.science/paper/U6CEVRAK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.7094&json=true","fetch_graph":"https://pith.science/api/pith-number/U6CEVRAKP6ASL64EEXXU2FOVVU/graph.json","fetch_events":"https://pith.science/api/pith-number/U6CEVRAKP6ASL64EEXXU2FOVVU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U6CEVRAKP6ASL64EEXXU2FOVVU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U6CEVRAKP6ASL64EEXXU2FOVVU/action/storage_attestation","attest_author":"https://pith.science/pith/U6CEVRAKP6ASL64EEXXU2FOVVU/action/author_attestation","sign_citation":"https://pith.science/pith/U6CEVRAKP6ASL64EEXXU2FOVVU/action/citation_signature","submit_replication":"https://pith.science/pith/U6CEVRAKP6ASL64EEXXU2FOVVU/action/replication_record"}},"created_at":"2026-05-18T02:37:44.673085+00:00","updated_at":"2026-05-18T02:37:44.673085+00:00"}