Theorem 10.2

Theorem 10.2 (Simultaneous batch compiler). Every transducer of Definition 10.1 whose initial record graph is fixed, finite, immutable, and pointer-closed compiles exactly and letter-synchronously into a finite scaffolding automaton of degree $$d=\max\{1,s+Aq\}$$ and observation/update distance at most $r+1$. The source transition uses only bounded labelled rooted unfoldings and does not branch on pointer identity; acceptance is in finite control.