{"paper":{"title":"Threshold phenomenon for the quintic wave equation in three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag","submitted_at":"2012-09-03T13:29:17Z","abstract_excerpt":"For the critical focusing wave equation $\\Box u = u^5$ on $\\R^{3+1}$ in the radial case, we establish the role of the \"center stable\" manifold $\\Sigma$ constructed in \\cite{KS} near the ground state $(W,0)$ as a threshold between type I blowup and scattering to zero, establishing a conjecture going back to numerical work by Bizo\\'n, Chmaj, Tabor. The underlying topology is stronger than the energy norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0347","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"}