{"paper":{"title":"Traceless $\\mathrm{SU}(2)$ characters and $\\mathbb{Z}/4$ instanton gradings for two-bridge and $(3,n)$-torus knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Bernd J. Wuebben","submitted_at":"2026-07-28T02:19:36Z","abstract_excerpt":"We assemble, and where possible independently verify, the representation-theoretic data underlying the pillowcase (symplectic) side of the Atiyah-Floer conjecture for knots, for two-bridge knots and $(3,n)$-torus knots. For a two-bridge knot $b(p,q)$ we give a short self-contained proof that every irreducible traceless $SU(2)$ representation is binary-dihedral; these are the $(p-1)/2$ dihedral characters at meridian angles $\\cos(2\\pi k/p)$, independent of $q$, and the traceless Riley polynomial is the explicit product $\\phi_p(u)=\\prod_k (u+4\\sin^2(\\pi k/p))$, monic of degree $(p-1)/2$ with con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26095","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/2607.26095/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"}