{"paper":{"title":"Solving the sextic by iteration: A study in complex geometry and dynamics","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Scott Crass","submitted_at":"1999-03-18T16:43:39Z","abstract_excerpt":"Recently, Peter Doyle and Curt McMullen devised an iterative solution to the fifth degree polynomial. At the method's core is a rational mapping of the Riemann sphere with the icosahedral symmetry of a general quintic. Moreover, this map posseses \"reliable\" dynamics: for almost any initial point, its trajectory converges to one of the periodic cycles that comprise an icosahedral orbit. This symmetry-breaking provides for a reliable or \"generally-convergent\" quintic-solving algorithm: with almost any fifth-degree equation, associate a rational map that has reliable dynamics and whose attractor "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9903111","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"}