{"paper":{"title":"Bosonization and Scale Invariance on Quantum Wires","arxiv_id":"hep-th/0611090","primary_cat":"hep-th","submitted_at":"2006-11-08T10:52:52+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13-20260917 on the question bank abstract-p1-20260923, exactly as returned. 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system.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.62,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.0,"background":0.04,"limitation":0.0,"future_work":0.0,"contribution":0.9,"interpretation":0.04}},{"i":4,"p":0.61,"id":"s4","own":true,"role":"result","text":"Using the associated scattering matrices, we give a complete classification of the critical points on a star graph with any number of edges.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.33,"quantitative":false,"quantitative_p":0.11,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.61,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.37,"interpretation":0.0}},{"i":5,"p":0.99,"id":"s5","own":true,"role":"result","text":"Critical points where the system is not invariant under wire permutations are 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