Static-Block Cellular Automata: Information Laws and Observable Languages

Information theory, dynamical systems, and formal logic often describe the same physical reality using incompatible languages. Here we introduce EBOC, a foundational framework that unifies subshifts of finite type, entropy theory, and observable semantics into a single coherent theory. The central contribution is a rigorous, discrete analogue of the \textbf{holographic principle}: we prove an explicit conditional-complexity bound (Theorem T4) showing that the information content of a bulk spacetime region is fully encoded in its causal thick boundary with only logarithmic overhead. Furthermore, we bridge the gap between simulation and verification by constructing explicit Büchi automata (Theorem T13) for the observable leaf languages of time-Markovizable systems. This turns dynamical questions traditionally solved by simulation into checking properties of formal languages. By reconciling the static geometry of ``block universes'' with the operational limits of observers, EBOC offers a portable toolkit for proving complexity bounds in physics and for verifying emergent properties in complex computational systems.