{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ZH4CIR5FMRRSQAE67L7WGHM2K4","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":"e840fe6664c6418969057c337119934d071a6f4363a50f26821de1c0665846c2","cross_cats_sorted":["hep-th","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-05-31T20:12:47Z","title_canon_sha256":"14bcf8d4326c6a402b299337687bf2ee4f50f44bf0009633e1fa87ba2ec4d168"},"schema_version":"1.0","source":{"id":"2406.00175","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.00175","created_at":"2026-07-05T08:25:58Z"},{"alias_kind":"arxiv_version","alias_value":"2406.00175v1","created_at":"2026-07-05T08:25:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.00175","created_at":"2026-07-05T08:25:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZH4CIR5FMRRS","created_at":"2026-07-05T08:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"ZH4CIR5FMRRSQAE6","created_at":"2026-07-05T08:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"ZH4CIR5F","created_at":"2026-07-05T08:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:6187168c7eb6c2346211c85acdb5d7c62785e76f62223db50dbaed8d1e6d61a1","target":"graph","created_at":"2026-07-05T08:25:58Z","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/2406.00175/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the space of monodromy data of second order $q$-difference equations through the framework of WKB analysis. We compute the connection matrices associated to the Stokes phenomenon of WKB wavefunctions and develop a general framework to parameterize monodromies of $q$-difference equations. Computations of monodromies are illustrated with explicit examples, including a $q$-Mathieu equation and its degenerations. In all examples we show that the monodromy around the origin of $\\mathbb{C}^*$ admits an expansion in terms of Voros symbols, or exponentiated quantum periods, with int","authors_text":"Fabrizio Del Monte, Pietro Longhi","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-05-31T20:12:47Z","title":"Monodromies of Second Order $q$-difference Equations from the WKB Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.00175","kind":"arxiv","version":1},"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":"sha256:32c1af249a7a45e515166a55cb9b60f3f65421c6581d8e4b1d66fb30907841cf","target":"record","created_at":"2026-07-05T08:25:58Z","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":"e840fe6664c6418969057c337119934d071a6f4363a50f26821de1c0665846c2","cross_cats_sorted":["hep-th","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-05-31T20:12:47Z","title_canon_sha256":"14bcf8d4326c6a402b299337687bf2ee4f50f44bf0009633e1fa87ba2ec4d168"},"schema_version":"1.0","source":{"id":"2406.00175","kind":"arxiv","version":1}},"canonical_sha256":"c9f82447a5646328009efaff631d9a571f34832445839295769180079954ac2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9f82447a5646328009efaff631d9a571f34832445839295769180079954ac2a","first_computed_at":"2026-07-05T08:25:58.079435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:25:58.079435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t3jUKycn70qYbm6C6aCLwv6II27iGpa9FclNWUC93qOh0oxSj3lkvv3DwEx66VKJGCGHL05TZSAWTTvQurwHDg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:25:58.079966Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.00175","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32c1af249a7a45e515166a55cb9b60f3f65421c6581d8e4b1d66fb30907841cf","sha256:6187168c7eb6c2346211c85acdb5d7c62785e76f62223db50dbaed8d1e6d61a1"],"state_sha256":"c832e3a58ee2b7ad07e0a7cf30bb8785e421dc2e18616549ee779ed14c53e305"}