$E$ is similar to $F$ but scaled by a factor 1/3.
Thus $E$ is similar to $F$ with a scale factor 1/3.
The only additional feature is the appearance of a factor of 2.
Thus we need only alter our constants by a factor of 2 to deal with this case.
This accounts for the factor 1/2 in (4).
The map $f$ factors through the space $X$.
We can factor $g$ into a product of irreducible elements.