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Question on Bodoff's capital allocation by percentile layer

I am going through Bodoff's paper, in section 6.2 and 6.3 of his paper, he gave formulas for the horizontal approach, and vertical approach.

I just want to confirm my understanding, the formulas as given in the paper essentially is allocating capital to the entire layer (e.g. there is only 1 layer)

If we were to allocate capital to a partial layer, for example the layer of VaR(50%) to Var(51%), then the range of the y would be between .5 to .51, rather than the 0 to VaR(99%) as provided in the paper?