{"paper":{"title":"On the factorization of composite polymer knots into separated prime components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Luca Tubiana","submitted_at":"2014-02-12T13:49:31Z","abstract_excerpt":"Using Monte Carlo simulations and advanced knot localization methods, we analyze the length and distribution of prime components in composite knots tied on Freely Jointed Rings (FJRs). For increasing contour length, we observe the progressive factorization of composite knots into separated prime components. However, we observe that a complete factorization, equivalent to the \"decorated ring\" picture, is not obtained even for rings of contour lengths $N\\simeq 3N_0$, about tens of times the most probable length of the prime knots tied on the rings. The decorated ring hypothesis has been used in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2819","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":""},"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"}