{"paper":{"title":"Proof of the Dubrovin conjecture and analysis of the tritronqu\\'ee solutions of $P_I$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"M. Huang, O. Costin, S. Tanveer","submitted_at":"2012-09-05T15:11:24Z","abstract_excerpt":"We show that the tritronqu\\'ee solution of the Painlev\\'e equation $\\P1$, $ y\"=6y^2+z$ which is analytic for large $z$ with $ \\arg z \\in (-\\frac{3\\pi}{5}, \\pi)$ is pole-free in a region containing the full sector ${z \\ne 0, \\arg z \\in [-\\frac{3\\pi}{5}, \\pi]}$ and the disk ${z: |z| < 37/20}$. This proves in particular the Dubrovin conjecture, an open problem in the theory of Painlev\\'e transcendents. The method, building on a technique developed in Costin, Huang, Schlag (2012), is general and constructive. As a byproduct, we obtain the value of the tritronqu\\'ee and its derivative at zero withi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1009","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"}