{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WB55PN2MISGTN2VN7W2UOOAGRA","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":"dd538caee8b42957f401394a241fc41118d26faf6b8a2fd95b52a9b625154525","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2026-06-26T20:11:35Z","title_canon_sha256":"dcfa5171dfa46dfa65bf39a5e0f70f194c3b2f4c5dba22f8e0d5dd4e2a192fab"},"schema_version":"1.0","source":{"id":"2606.28579","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28579","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28579v1","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28579","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"pith_short_12","alias_value":"WB55PN2MISGT","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"pith_short_16","alias_value":"WB55PN2MISGTN2VN","created_at":"2026-06-30T00:15:19Z"},{"alias_kind":"pith_short_8","alias_value":"WB55PN2M","created_at":"2026-06-30T00:15:19Z"}],"graph_snapshots":[{"event_id":"sha256:14ec05222c9a04c75428c04e9a59684d59b66e1707773ca424ca1ff202f872d1","target":"graph","created_at":"2026-06-30T00:15:19Z","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/2606.28579/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider solutions of the sinh-Gordon Painlev\\'e III equation \\[ u_{xx} + \\frac{1}{x} u_x = \\sinh u \\] that are real on $(0,\\infty)$. They are parametrized by the monodromy parameter $p\\in\\overline{\\mathbb{C}}$, $|p|>1$, and an additional real parameter $s^{\\mathbb{R}}$ when $p=\\infty$. Our previous joint work with A. Its described the asymptotic behavior of these solutions as $x\\to\\infty$. Here, we describe the transition as $x, p\\to \\infty$, $2\\Im(p)=-s^{\\mathbb R}$, between singular solutions ($|p|<\\infty$) and smooth solutions ($p=\\infty$). In short, if we parametrize $|p|^2 = 1 + e^{2\\","authors_text":"Kenta Miyahara, Maxim L. Yattselev","cross_cats":["math-ph","math.CA","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2026-06-26T20:11:35Z","title":"Transition asymptotics for the real solutions of the sinh-Gordon Painlev\\'e III equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28579","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":"sha256:933fb8009231d3d7d74fe2da3f2d3f9196182e9d23f0512e50b44bcb310b5796","target":"record","created_at":"2026-06-30T00:15:19Z","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":"dd538caee8b42957f401394a241fc41118d26faf6b8a2fd95b52a9b625154525","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2026-06-26T20:11:35Z","title_canon_sha256":"dcfa5171dfa46dfa65bf39a5e0f70f194c3b2f4c5dba22f8e0d5dd4e2a192fab"},"schema_version":"1.0","source":{"id":"2606.28579","kind":"arxiv","version":1}},"canonical_sha256":"b07bd7b74c448d36eaadfdb5473806880375572ef3385c188d8a76dd01f772af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b07bd7b74c448d36eaadfdb5473806880375572ef3385c188d8a76dd01f772af","first_computed_at":"2026-06-30T00:15:19.704011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T00:15:19.704011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DC6gHjprC7EAFtwKzbd+PTrBVp5EeWZIquOexgcB1wjbzYqw9UzAKi2GKLWCz1NloG1ZQH6bg4X/qFynZ7GzCg==","signature_status":"signed_v1","signed_at":"2026-06-30T00:15:19.704411Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.28579","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:933fb8009231d3d7d74fe2da3f2d3f9196182e9d23f0512e50b44bcb310b5796","sha256:14ec05222c9a04c75428c04e9a59684d59b66e1707773ca424ca1ff202f872d1"],"state_sha256":"1c52a294320cdbe80a4216e0e0722809ab868aa6bc6dbf477955fd2e18e6b49d"}