Quick overview of approach:
Concerning numbers that are right-derivable (i.e., that have a derivation that ends in 1)
first: that one can double the number by taking two left branches
second: that one can triple the number by taking three left branches
third: that one can multiply the number by five by taking three lefts branches and then a right.
Once one has taken the three left and one right branch, all numbers encountered thereafter will be multiples of alpha, hence the theorem:
Theorem 3.4. Given integers m and n where m is right-derivable and n is in the right tree, then the product mn can be expressed as a simple concatenation of the expressions of m and n.