{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FVC4H25RA7MHCSPB7KHYFOZMBB","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":"e69b46edc72c2183cccd0d441e58f0a61e6fcae52a1ca9739f32a71d916e2789","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-05T09:30:47Z","title_canon_sha256":"ced6303dcd705508fd582ef5688c481b0855599e2e89f2330996b06be522efed"},"schema_version":"1.0","source":{"id":"1908.01532","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01532","created_at":"2026-07-05T00:37:46Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01532v2","created_at":"2026-07-05T00:37:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01532","created_at":"2026-07-05T00:37:46Z"},{"alias_kind":"pith_short_12","alias_value":"FVC4H25RA7MH","created_at":"2026-07-05T00:37:46Z"},{"alias_kind":"pith_short_16","alias_value":"FVC4H25RA7MHCSPB","created_at":"2026-07-05T00:37:46Z"},{"alias_kind":"pith_short_8","alias_value":"FVC4H25R","created_at":"2026-07-05T00:37:46Z"}],"graph_snapshots":[{"event_id":"sha256:ea4b6be532e45a8003936715fdcb6253cdb3a6fdd7ad2d4cc0fc2e56e586d903","target":"graph","created_at":"2026-07-05T00:37:46Z","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/1908.01532/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a family of tronqu\\'{e}e solutions of the Painelv\\'{e} II equation \\begin{equation*} q''(s)=2q(s)^3+sq(s)-(2\\alpha+\\frac12), \\qquad \\alpha > -\\frac12, \\end{equation*} which is characterized by the Stokes multipliers $$s_1=-e^{-2\\alpha \\pi i },\\quad s_2=\\omega, \\quad s_3=-e^{2 \\alpha \\pi i} $$ with $\\omega$ being a free parameter. These solutions include the well-known generalized Hastings-McLeod solution as a special case if $\\omega=0$. We derive asymptotics of integrals of the tronqu\\'{e}e solutions and the associated Hamiltonians over the real axis for $\\alpha > -1/2$ and $\\omega","authors_text":"Dan Dai, Lun Zhang, Shuai-Xia Xu","cross_cats":["math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-05T09:30:47Z","title":"On integrals of the tronqu\\'{e}e solutions and the associated Hamiltonians for the Painlev\\'{e} II equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01532","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":"sha256:0ee4bb93b792f348d98e1f8d9baa3f5aae5ce0bab39a86f2c75b87da9d0cd75a","target":"record","created_at":"2026-07-05T00:37:46Z","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":"e69b46edc72c2183cccd0d441e58f0a61e6fcae52a1ca9739f32a71d916e2789","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-05T09:30:47Z","title_canon_sha256":"ced6303dcd705508fd582ef5688c481b0855599e2e89f2330996b06be522efed"},"schema_version":"1.0","source":{"id":"1908.01532","kind":"arxiv","version":2}},"canonical_sha256":"2d45c3ebb107d87149e1fa8f82bb2c085f9747955eeb9cc52b49b84b5e6d53da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d45c3ebb107d87149e1fa8f82bb2c085f9747955eeb9cc52b49b84b5e6d53da","first_computed_at":"2026-07-05T00:37:46.616388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:37:46.616388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dO8ig2I5O68LUVWqQzyx+VAP5Uo1b6dElLz7/WH06fq85E/WTEeM09qsBEskDA4i2sB+hadwmQP28cKZUalCDA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:37:46.616865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.01532","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ee4bb93b792f348d98e1f8d9baa3f5aae5ce0bab39a86f2c75b87da9d0cd75a","sha256:ea4b6be532e45a8003936715fdcb6253cdb3a6fdd7ad2d4cc0fc2e56e586d903"],"state_sha256":"962ac7eb8d0e1f422f1754b856e7b148b3a8359e5e3315cd70c3b541c53e55c0"}