The destiny of constant structure discrete time closed semantic systems

Constant structure closed semantic systems are the systems each element of which receives its definition through the correspondent unchangeable set of other elements of the system. Discrete time means here that the definitions of the elements change iteratively and simultaneously based on the "neighbor portraits" from the previous iteration. I prove that the iterative redefinition process in such class of systems will quickly degenerate into a series of pairwise isomorphic states and discuss some directions of further research.