{"paper":{"title":"Concrete Solution to the Nonsingular Quartic Binary Moment Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Raul E. Curto, Seonguk Yoo","submitted_at":"2014-12-26T02:35:00Z","abstract_excerpt":"Given real numbers $\\beta \\equiv \\beta ^{\\left( 4\\right) }\\colon \\beta_{00}$, $\\beta _{10}$, $\\beta _{01}$, $\\beta _{20}$, $\\beta _{11}$, $ \\beta _{02}$, $\\beta _{30}$, $\\beta _{21}$, $\\beta _{12}$, $\\beta _{03}$, $\\beta _{40}$, $\\beta _{31}$, $\\beta _{22}$, $\\beta _{13}$, $\\beta _{04}$, with $\\beta _{00} >0$, the quartic real moment problem for $\\beta $ entails finding conditions for the existence of a positive Borel measure $\\mu $, supported in $\\mathbb{R}^2$, such that $\\beta _{ij}=\\int s^{i}t^{j}\\,d\\mu \\;\\;(0\\leq i+j\\leq 4) $. Let $\\mathcal{M}(2)$ be the 6 x 6 moment matrix for $\\beta^{(4)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7882","kind":"arxiv","version":1},"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"}