Corollary: Finite structural stabilization

Along every infinite discrete trajectory with permanent scars on a finite coordinate universe, the scar set changes nontrivially at most $N_W-C_0$ times and is eventually constant. There is no common bound on the time of its last change without an additional waiting-time assumption. Weights, biases, and active masks can continue changing.

Proof. Each strict change adds at least one new coordinate to a nondecreasing set of cardinality at most $N_W$. There can be only finitely many such changes. The discrete times of those finitely many changes have a finite maximum, although arbitrarily long delays are permitted.