Below I use the approach of producing numbers using the null set to try to demonstrate this. The page horizontal isomorphic links on the right hand side are the usual ones. The page vertical isomorphic links are the ones I have used in my model. The rest of the string determines the associated state of the vertical isomorphism. The current state of a vertical isomorphism is the active link for that isomorphism.
All inactive links are either past or future states of isomorphisms.
The self contained FAS of a particular vertical isomorphism determines which links are acceptable immediate successor states of that isomorphism. Depending on the nature of the FAS there could be more than one acceptable immediate successor state for that isomorphism. Neither the anisomorphic null set nor the isomorphism tree since they both contain no information can internally address the unavoidable question of their own durability. In order for a vertical isomorphic link to transfer to another string both the current link and an acceptable successor link must be simultaneously active. The transfer inactivates the prior link.