{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JKLAJ5M445MDXVL3A3VQ7KKEHD","short_pith_number":"pith:JKLAJ5M4","schema_version":"1.0","canonical_sha256":"4a9604f59ce7583bd57b06eb0fa94438da49057d07b5dcd0ea47a70e9f293709","source":{"kind":"arxiv","id":"1306.6161","version":2},"attestation_state":"computed","paper":{"title":"On the tritronqu\\'ee solutions of P$_I^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"A. Kapaev, C. Klein, T. Grava","submitted_at":"2013-06-26T08:24:01Z","abstract_excerpt":"For equation P$_I^2$, the second member in the P$_I$ hierarchy, we prove existence of various degenerate solutions depending on the complex parameter $t$ and evaluate the asymptotics in the complex $x$ plane for $|x|\\to\\infty$ and $t=o(x^{2/3})$. Using this result, we identify the most degenerate solutions $u^{(m)}(x,t)$, $\\hat u^{(m)}(x,t)$, $m=0,...,6$, called {\\em tritronqu\\'ee}, describe the quasi-linear Stokes phenomenon and find the large $n$ asymptotics of the coefficients in a formal expansion of these solutions. We supplement our findings by a numerical study of the tritronqu\\'ee solu"},"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":"1306.6161","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-26T08:24:01Z","cross_cats_sorted":["math.CA","math.MP"],"title_canon_sha256":"fd6b284ed26fb484bce19824590bb07f3561718777aab8b1490c4530478baedc","abstract_canon_sha256":"309dd6bf2c34509fe2e713f1f473a4e8f81bdc16bbd5c55ed55d8bddace86e7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:52.007091Z","signature_b64":"h9D4oQA+o/Gg/CIEom1gJGzdu/+apoZBR6RIWqpBJi4P6rvSUsY94kyCVZN2QkHhZsuhJ+I5409v1J01LRrFBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a9604f59ce7583bd57b06eb0fa94438da49057d07b5dcd0ea47a70e9f293709","last_reissued_at":"2026-05-18T02:21:52.006479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:52.006479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the tritronqu\\'ee solutions of P$_I^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"A. Kapaev, C. Klein, T. Grava","submitted_at":"2013-06-26T08:24:01Z","abstract_excerpt":"For equation P$_I^2$, the second member in the P$_I$ hierarchy, we prove existence of various degenerate solutions depending on the complex parameter $t$ and evaluate the asymptotics in the complex $x$ plane for $|x|\\to\\infty$ and $t=o(x^{2/3})$. Using this result, we identify the most degenerate solutions $u^{(m)}(x,t)$, $\\hat u^{(m)}(x,t)$, $m=0,...,6$, called {\\em tritronqu\\'ee}, describe the quasi-linear Stokes phenomenon and find the large $n$ asymptotics of the coefficients in a formal expansion of these solutions. We supplement our findings by a numerical study of the tritronqu\\'ee solu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6161","kind":"arxiv","version":2},"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":"1306.6161","created_at":"2026-05-18T02:21:52.006597+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.6161v2","created_at":"2026-05-18T02:21:52.006597+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.6161","created_at":"2026-05-18T02:21:52.006597+00:00"},{"alias_kind":"pith_short_12","alias_value":"JKLAJ5M445MD","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JKLAJ5M445MDXVL3","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JKLAJ5M4","created_at":"2026-05-18T12:27:49.015174+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JKLAJ5M445MDXVL3A3VQ7KKEHD","json":"https://pith.science/pith/JKLAJ5M445MDXVL3A3VQ7KKEHD.json","graph_json":"https://pith.science/api/pith-number/JKLAJ5M445MDXVL3A3VQ7KKEHD/graph.json","events_json":"https://pith.science/api/pith-number/JKLAJ5M445MDXVL3A3VQ7KKEHD/events.json","paper":"https://pith.science/paper/JKLAJ5M4"},"agent_actions":{"view_html":"https://pith.science/pith/JKLAJ5M445MDXVL3A3VQ7KKEHD","download_json":"https://pith.science/pith/JKLAJ5M445MDXVL3A3VQ7KKEHD.json","view_paper":"https://pith.science/paper/JKLAJ5M4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.6161&json=true","fetch_graph":"https://pith.science/api/pith-number/JKLAJ5M445MDXVL3A3VQ7KKEHD/graph.json","fetch_events":"https://pith.science/api/pith-number/JKLAJ5M445MDXVL3A3VQ7KKEHD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JKLAJ5M445MDXVL3A3VQ7KKEHD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JKLAJ5M445MDXVL3A3VQ7KKEHD/action/storage_attestation","attest_author":"https://pith.science/pith/JKLAJ5M445MDXVL3A3VQ7KKEHD/action/author_attestation","sign_citation":"https://pith.science/pith/JKLAJ5M445MDXVL3A3VQ7KKEHD/action/citation_signature","submit_replication":"https://pith.science/pith/JKLAJ5M445MDXVL3A3VQ7KKEHD/action/replication_record"}},"created_at":"2026-05-18T02:21:52.006597+00:00","updated_at":"2026-05-18T02:21:52.006597+00:00"}