Axiomatic Characterization of Universe\\ as Quantum Cellular Automaton:\\ QCA Implementation of Computational Universe Terminal Object\\ and Unified Time Scale Limit

In previous series on ``computational universe'' U_{comp} = (X,T,C,I), we have constructed discrete complexity geometry, discrete information geometry, control manifold (M,G) induced by unified time scale, task information manifold (S_Q,g_Q), time--information--complexity joint variational principle, multi-observer consensus geometry, causal diamonds and Null--Modular double cover, topological complexity and undecidability, and unified computational universe terminal object U_{comp}^{term}. On other hand, quantum cellular automaton (QCA) long viewed as natural candidate model for ``universe as quantum discrete dynamical system'': on countable lattice sites, each site carries finite-dimensional Hilbert space, overall evolution is local unitary update. Traditional QCA theory mainly focused on information propagation speed, reversibility and universality, less systematically integrated with unified time scale, complexity geometry and universe terminal object structure. This paper gives rigorous axiomatic characterization of viewpoint ``universe as quantum cellular automaton'' within unified time scale--computational universe terminal object framework. Main results: enumerate \item Introduce ``universe QCA object'' U_{QCA} = (\Lambda,{H_x}_{x\in\Lambda}, U, C_T), where \Lambda countable lattice site set, H_x local Hilbert space, U global unitary update satisfying locality and reversibility, C_T unified time scale cost of one update. We propose QCA universe axioms: local finiteness, unified time scale compatibility, observable operator network and causal structure, embeddability in computational universe axioms. \item Construct functor from QCA universe objects to computational universe objects U_{comp} = (X,T,C,I), and functor from physically realizable computational universe to QCA universe, prove under unified time scale and locality axioms, these two functors give categorical equivalence on appropriately defined subcategories: $ QCAUniv^{phys} \simeq CompUniv^{phys}. In particular, unified computational universe terminal object U_{comp}^{term} restriction on QCA subcategory isomorphic to ``universe QCA terminal object'' U_{QCA}^{term}. \item Under unified time scale master scale, construct control manifold (M,G) and continuous limit for QCA universe: prove under Lieb--Robinson bounded propagation speed and controllable perturbation conditions, exists continuous time limit family U(t) and effective Hamiltonian H_{eff} such that unified time scale density \kappa(\omega) connects with QCA discrete spectral data through scattering--spectral shift--group delay formula. \item From within QCA universe construct observers, causal diamonds, Null--Modular double cover and time crystals, prove these structures can be completely realized on QCA Hilbert space: observers are local subsystems on QCA, causal diamonds are local space--time blocks, Null--Modular Z_2$ holonomy and time crystal phase parity structure realized through constructing self-reference feedback network and Floquet--QCA on QCA. \item At topological complexity and undecidability level, prove QCA universe contains all computable discrete dynamical systems: any constructible computational universe object can be embedded in some QCA universe; thus topological loop contraction undecidability, catastrophic safety undecidability, and capability--risk frontier non-algorithmic solvability previously proved at computational universe level all hold in QCA universe. enumerate This paper thus shows: ``universe as quantum cellular automaton'' not independent additional assumption from computational universe framework, but concrete implementation of unified computational universe terminal object in particularly natural subcategory; unified time scale, complexity geometry, information geometry, multi-observer causal network and capability--risk structure can be completely realized and concretely engineered in QCA universe.