{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:2JZVEC4YDGKRCF6B3LYRMCCEJL","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":"adb761bd388648765800491dfef2dced0926c841a243f2f1aab2fefbcf5b510e","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-08-14T17:54:01Z","title_canon_sha256":"5d4bdc41417dfa8e374be73eb0ae935cdfd3c4451f517ebc6a195d795d4d0577"},"schema_version":"1.0","source":{"id":"2008.06492","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.06492","created_at":"2026-07-05T06:17:35Z"},{"alias_kind":"arxiv_version","alias_value":"2008.06492v2","created_at":"2026-07-05T06:17:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.06492","created_at":"2026-07-05T06:17:35Z"},{"alias_kind":"pith_short_12","alias_value":"2JZVEC4YDGKR","created_at":"2026-07-05T06:17:35Z"},{"alias_kind":"pith_short_16","alias_value":"2JZVEC4YDGKRCF6B","created_at":"2026-07-05T06:17:35Z"},{"alias_kind":"pith_short_8","alias_value":"2JZVEC4Y","created_at":"2026-07-05T06:17:35Z"}],"graph_snapshots":[{"event_id":"sha256:c9bf8992921cfef9399f1b5ca58e607675384b41b03787a885356ae80249c85f","target":"graph","created_at":"2026-07-05T06:17:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.06492/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The singularly perturbed Riccati equation is the first-order nonlinear ODE $\\hbar \\partial_x f = af^2 + bf + c$ in the complex domain where $\\hbar$ is a small complex parameter. We prove an existence and uniqueness theorem for exact solutions with prescribed asymptotics as $\\hbar \\to 0$ in a halfplane. These exact solutions are constructed using the Borel-Laplace method; i.e., they are Borel summations of the formal divergent $\\hbar$-power series solutions. As an application, we prove existence and uniqueness of exact WKB solutions for the complex one-dimensional Schr\\\"odinger equation with a ","authors_text":"Nikita Nikolaev","cross_cats":["math-ph","math.CV","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-08-14T17:54:01Z","title":"Exact Solutions for the Singularly Perturbed Riccati Equation and Exact WKB Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.06492","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:bd59efa7bd8aa88354265ecec58e9022721c9b08fcde5e984406aa78d343a192","target":"record","created_at":"2026-07-05T06:17:35Z","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":"adb761bd388648765800491dfef2dced0926c841a243f2f1aab2fefbcf5b510e","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-08-14T17:54:01Z","title_canon_sha256":"5d4bdc41417dfa8e374be73eb0ae935cdfd3c4451f517ebc6a195d795d4d0577"},"schema_version":"1.0","source":{"id":"2008.06492","kind":"arxiv","version":2}},"canonical_sha256":"d273520b9819951117c1daf11608444ac0ce47c0b937c4b1b26678216af3a646","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d273520b9819951117c1daf11608444ac0ce47c0b937c4b1b26678216af3a646","first_computed_at":"2026-07-05T06:17:35.341360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:17:35.341360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MGhqr5BI4BgyS4borQLxsYVtq2TA+5FUIrwRKJkVFmT01dpwuPFYGu60FC1Dd6ISuaamVgNxh8vWmCAVzGFMCw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:17:35.341821Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.06492","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd59efa7bd8aa88354265ecec58e9022721c9b08fcde5e984406aa78d343a192","sha256:c9bf8992921cfef9399f1b5ca58e607675384b41b03787a885356ae80249c85f"],"state_sha256":"3706a1dc89f80c045cb471d452a7fa47c2ce808039dfa0a2a2a05da7b437be23"}