{"paper":{"title":"Wall Crossing Invariants: from quantum mechanics to knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A.Mironov, A.Morozov, D.Galakhov","submitted_at":"2014-10-30T18:23:01Z","abstract_excerpt":"We offer a pedestrian level review of the wall-crossing invariants. The story begins from the scattering theory in quantum mechanics where the spectrum reshuffling can be related to permutations of S-matrices. In non-trivial situations, starting from spin chains and matrix models, the S-matrices are operator-valued and their algebra is described in terms of R- and mixing (Racah) U-matrices. Then, the Kontsevich-Soibelman invariants are nothing but the standard knot invariants made out of these data within the Reshetikhin-Turaev-Witten approach. The R- and Racah matrices acquire a relatively un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8482","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"}