{"paper":{"title":"A proof of Wright's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jan Bouwe van den Berg, Jonathan Jaquette","submitted_at":"2017-03-31T19:29:24Z","abstract_excerpt":"Wright's conjecture states that the origin is the global attractor for the delay differential equation $y'(t) = - \\alpha y(t-1) [ 1 + y(t) ] $ for all $\\alpha \\in (0,\\tfrac{\\pi}{2}]$. This has been proven to be true for a subset of parameter values $\\alpha$. We extend the result to the full parameter range $\\alpha \\in (0,\\tfrac{\\pi}{2}]$, and thus prove Wright's conjecture to be true. Our approach relies on a careful investigation of the neighborhood of the Hopf bifurcation occurring at $\\alpha =\\tfrac{\\pi}{2}$. This analysis fills the gap left by complementary work on Wright's conjecture, whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00029","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"}