{"paper":{"title":"Zeroes of the Jones polynomial","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"F. Y. Wu, J. Wang","submitted_at":"2001-05-01T20:32:32Z","abstract_excerpt":"We study the distribution of zeroes of the Jones polynomial $V_K(t)$ for a knot $K$. We have computed numerically the roots of the Jones polynomial for all prime knots with $N\\leq 10$ crossings, and found the zeroes scattered about the unit circle $|t|=1$ with the average distance to the circle approaching a nonzero value as $N$ increases.\n  For torus knots of the type $(m,n)$ we show that all zeroes lie on the unit circle with a uniform density in the limit of either $m$ or $n\\to \\infty$, a fact confirmed by our numerical findings. We have also elucidated the relation connecting the Jones pol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0105013","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cond-mat/0105013/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"}