Theorem 9.2

Theorem 9.2 (Simultaneous-batch compiler; fixed virtual initialization). Every bounded simultaneous record transducer with parameters $(s,A,q,r)$, one fixed finite immutable pointer-closed initial graph, and plans determined by finite control, the input letter and bounded labelled rooted unfoldings has an exact letter-synchronous native scaffolding-automaton implementation of degree $$d=\max\{1,s+Aq\}$$ and observation/update distance at most $r+1$. Physical pointer identity is not an observable test; fixed initial records are virtual finite decoder data.