{"paper":{"title":"Principal graph stability and the jellyfish algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"David Penneys, Stephen Bigelow","submitted_at":"2012-08-08T02:30:52Z","abstract_excerpt":"We show that if the principal graph of a subfactor planar algebra of modulus \\delta>2 is stable for two depths, then it must end in A_{finite} tails. This result is analogous to Popa's theorem on principal graph stability. We use these theorems to show that an (n-1) supertransitive subfactor planar algebra has jellyfish generators at depth n if and only if its principal graph is a spoke graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1564","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"}