I study deterministic local finite-speed systems as a general framework for spatially distributed physical and computational processes under strict locality constraints. A central question is whether locality fundamentally limits the coexistence of predictability, robustness, and large-scale distributed information capacity. I first show that locality alone imposes no global restriction: information may be serialized through bounded-width conduits, effectively reducing the system to a low-dimensional communication channel. I then identify a distinct structural regime in which information remains genuinely distributed and independently controllable across space. In this regime, separator-based geometric reduction confines cross-system dependencies to bounded-width slabs that admit planar coarse representations. Planar topology then imposes non-crossing constraints, excluding alternating connection patterns and inducing a binary exclusion principle at separator scale. When this exclusion aligns with independently controllable separator variables on a positive-density subset, I prove that the realizable configuration space collapses exponentially relative to the formal binary cube, yielding a linear lower bound on the factorization defect. I establish this obstruction unconditionally in restricted regimes where control and topology are co-localized, and conditionally in general systems under a transfer-realizable control hypothesis. Deriving this transfer mechanism from locality and predictive structure remains an open problem. These results isolate a precise geometric-combinatorial bottleneck governing the coexistence of locality, distributed control, and large-scale information capacity.
Imran Ali Raza (Mon,) studied this question.