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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.26095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-07-28T02:19:36Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"7d53d2974601101b6d139996a64280ffac8ca73d0711aa09727e004b09ff39c0","abstract_canon_sha256":"904bc8da8176441c677e24534f0161c4fc42270aa9376b55683952d3fc48bc13"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec8654017a740fe4db676853401bdc1eedc729b133a0b01075cc6a98ab97cfa9","last_reissued_at":"2026-07-30T00:08:20.333229Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-30T00:08:20.333229Z"},"graph_snapshot":{"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. 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