Boundary Observability Posting

This record presents a reproducible computational framework for studying attractor-basin observability in finite deterministic dynamical systems under restricted local observation. The central problem is whether the eventual attractor basin of an initial state can be identified from a finite spatiotemporal history observed only at a selected subset of system variables. The framework combines exhaustive state-space enumeration, exact attractor and basin identification, restricted observation histories, Bayes-optimal classification, information-theoretic quantities, boundary descriptors, perturbation detectability, and direct overlap between histories generated by different basins. The methodology is evaluated on two finite dynamical-system classes. The first benchmark includes all 256 elementary cellular automata on a periodic seven-cell ring, with complete enumeration of all 128 initial states. The second experiment evaluates 100 synchronous random Boolean networks with seven nodes and two inputs per node. The results show that global basin and transition-graph descriptors can predict observability strongly within the elementary cellular automata class, but the same structural relationships generalize poorly to random Boolean networks. Boundary topology and perturbation detectability provide additional information, but only partially explain the remaining classification difficulty. Direct overlap between observation histories generated by different attractor basins provides the clearest description of irreducible ambiguity. The work does not propose a new entropy measure, classifier, or universal law of observability. Its contribution is methodological and computational: it provides an exact and reproducible protocol for comparing global dynamics, observation boundaries, finite observation horizons, and Bayes-optimal attractor-basin classification. This Zenodo record contains the manuscript, LaTeX source, and publication figures. The reported results apply to the finite system sizes, observation boundaries, and observation horizons tested in the study.