User blog comment:Syst3ms/A formal interpretation of Y sequence : F sequence/@comment-35470197-20190810061448

In order to go beyond (1,3) in Y sequence and (0,3) in N primitive, you need to expand difference sequences in another direction. For example, N primitive expands the sequence given by the leftmost entries of difference sequences. Otherwise, they are bounded by BMS.

By the way, I guess that your reconstruction step is wrong, because it ignores intermediate values which are not used to define the difference sequences.