{"paper":{"title":"A doubled Gordon threshold for palindromic quasiperiodic Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Wencai Liu","submitted_at":"2026-07-27T09:07:52Z","abstract_excerpt":"We consider one-frequency quasiperiodic Schr\\\"odinger operators \\[ (H_{v,\\alpha,\\theta}u)(n) =\nu(n+1)+u(n-1) +\nv(\\theta+n\\alpha)u(n) \\] acting on $\\ell^2(\\mathbb Z)$, where $\\alpha\\notin\\mathbb Q$ and $v\\in C^2(\\mathbb T,\\mathbb R)$ is an even function. We develop a new Gordon-type method that exploits approximate repetitions and palindromic symmetries simultaneously. Denote by $L(E)$ the Lyapunov exponent and let\n  \\[\\beta(\\alpha) =\n\\limsup_{|k|\\to\\infty} -\\frac{\\log\\|k\\alpha\\|_{\\mathbb R/\\mathbb Z}}{|k|}. \\] We prove that, for every completely resonant phase $2\\theta\\in\\alpha\\mathbb Z+\\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24188","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.24188/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}