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We note an implication of chiral Luttinger liquid based edge statedescription of the fractional quantum Hall effect. By considering severalexamples that involve backward moving neutral modes, arising from eithercomposite fermions with reverse flux attached or edge reconstruction, we showthat non-universality of the edge exponent implies non-universality of the Hallconductance, as measured in the two-terminal conductance.

Universality Lost: Relation between quantizations of the Hall conductance and the edge exponents in fractional quantum Hall effect