{"paper":{"title":"Boundedness of Dehn surgery slopes admitting hyperbolic $\\mathrm{PSL}(2,\\mathbb{R})$-representations for two-bridge knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ran Tao, Shunjiang Jiang","submitted_at":"2026-05-29T04:08:22Z","abstract_excerpt":"We study Dehn fillings on two-bridge knots via non-abelian representations into $\\mathrm{PSL}(2,\\mathbb{R})$ whose meridian image is hyperbolic. For each fixed nontrivial two-bridge knot, we prove that the set of surgery slopes admitting such representations is bounded. Equivalently, Dehn fillings along slopes with sufficiently large absolute value admit no non-abelian $\\mathrm{PSL}(2,\\mathbb{R})$ representations with hyperbolic meridian image. The proof combines the Riley polynomial with Khoi's surgery-slope formula. On each admissible real algebraic branch, we express the meridian and longit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30817","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/2605.30817/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"}