Before revision:  The core of this extended multifractal analysis is the non-monotonic behavior of the generalized Hurst exponent  -- the fundamental exponent of the study -- and hence a multi-branched spectrum of dimensions , which for our case is additionally of the left-sided one.
After revision:  The core of this extended multifractal analysis is the non-monotonic behavior of the generalized Hurst exponent h(q) -- the fundamental exponent of the study -- and hence a multi-branched spectrum of dimensions , which for our case is additionally of the left-sided one.