We formalize a constructive subclass of locality-preserving deterministic operators acting on graph-indexed state systems. We define the class of Bounded Local Generator Classes (BLGC), consisting of finite-range generators operating on bounded state spaces under deterministic composition. Within this class, incremental update cost is independent of total system dimension. We prove that, under the BLGC assumptions, per-step operator work satisfies W_t = O(1) as the number of nodes M \to \infty, establishing a structural decoupling between global state size and incremental computational effort. The framework admits a Hilbert-space embedding in \ell^2(V; \mathbb{R}^d) and yields bounded operator norms on admissible subspaces. The result applies specifically to the defined subclass and does not claim universality beyond the stated locality and boundedness constraints.

翻译：我们形式化地定义了一类作用于图索引状态系统的保持局部性的确定性算子的构造性子类。我们定义了有界局部生成器类（BLGC），该类由在确定性组合下作用于有界状态空间上的有限范围生成器组成。在此类中，增量更新成本与系统总维度无关。我们证明，在BLGC假设下，随着节点数M趋于无穷，每步算子工作量满足W_t = O(1)，从而确立了全局状态规模与增量计算工作量之间的结构解耦。该框架允许在\ell^2(V; \mathbb{R}^d)空间中进行希尔伯特空间嵌入，并在容许子空间上产生有界算子范数。该结果特别适用于所定义的子类，并不声称超出所述局部性和有界性约束的普适性。