{"paper":{"title":"On knots, complements, and 6j-symbols","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP"],"primary_cat":"hep-th","authors_text":"Hao Derrick Zhang, Hao Ellery Wang, Satoshi Nawata, Yuanzhe Jack Yang","submitted_at":"2020-12-22T13:50:24Z","abstract_excerpt":"This paper investigates the relation between colored HOMFLY-PT and Kauffman homology, $\\text{SO}(N)$ quantum $6j$-symbols and $(a,t)$-deformed $F_K$. First, we present a simple rule of grading change which allows us to obtain the $[r]$-colored quadruply-graded Kauffman homology from the $[r^2]$-colored quadruply-graded HOMFLY-PT homology for thin knots. This rule stems from the isomorphism of the representations $(\\mathfrak{so}_6,[r]) \\cong (\\mathfrak{sl}_4,[r^2])$. Also, we find the relationship among $A$-polynomials of SO and SU-type coming from a differential on Kauffman homology. Second, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.12008","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/2012.12008/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"}