Parameterized Universe Quantum Cellular Automaton Theory\\ Under Finite Information

Under framework of quantum cellular automaton (QCA), quasi-local operator algebra and finite information principle, this paper constructs class of explicitly parameterized ``universe quantum cellular automaton'' models. Core idea: assuming physically distinguishable information amount of physical universe has finite upper bound I_{\max}, then entire universe can be encoded as finite bit string parameter vector \Theta, uniquely determining universe-level QCA object under strict axiomatic system $ U_{QCA}(\Theta) = \bigl(\Lambda(\Theta),H_{cell}(\Theta),A(\Theta),\alpha_{\Theta},\omega_0^{\Theta}\bigr) where \Lambda(\Theta) finite lattice site set, H_{cell}(\Theta) cellular Hilbert space, A(\Theta) quasi-local C^\ast algebra, \alpha_{\Theta} automorphism with finite propagation radius (realized by finite-depth local unitary circuit), \omega_0^{\Theta} initial universe state generated by finite circuit. Under ``finite information universe axiom'', we introduce global information capacity upper bound I_{\max}, decompose universe parameter vector into structural parameters \Theta_{str}, dynamical parameters \Theta_{dyn} and initial state parameters \Theta_{ini}. Prove in QCA algebraic framework: for each finite bit string \Theta satisfying I_{param}(\Theta)+S_{\max}(\Theta)\le I_{\max}, exists universe QCA satisfying locality, reversibility and causal boundedness; where parameter information amount I_{param}(\Theta) and maximum von Neumann entropy S_{\max}(\Theta) of universe reachable Hilbert space satisfy I_{param}(\Theta)+S_{\max}(\Theta)\le I_{\max} thereby characterizing joint constraint of ``finite information'' on cell number, local Hilbert dimension and parameter precision. In continuous limit, construct class of scalable parameterized QCA family U_{QCA}(\Theta;a,\Delta t), in appropriate limit of lattice spacing a and time step \Delta t\to 0, prove convergence to effective field equations, including Dirac-type equation \bigl(i\gamma^\mu\partial_\mu - m(\Theta)\bigr)\psi = 0 and equation system with gauge coupling and effective metric parameters, where mass m(\Theta), gauge coupling and gravitational constant effective continuous parameters analytically derived from discrete angle parameters and structural data in \Theta_{dyn}. Furthermore, introduce observer network and causal feedback, define class of parameterized observer objects and consensus geometry at universe QCA level, making universe parameter \Theta simultaneously determine physical laws and observable statistical structure. Appendices give formalized construction of quasi-local C^\ast$ algebra and QCA; strict correspondence theorem between finite-depth local circuits and QCA automorphisms; systematic derivation of Dirac--QCA continuous limit; proof of bounds on finite information inequality and relationships among cell number and local dimension; and abstract map examples from parameter vector to effective field theory constants and observer network statistics. This paper thereby provides axiomatizable, computable and parameterized ``finite-information universe cellular automaton'' theoretical framework, establishing mathematical foundation for viewing physical universe as quantum computation process with finite description complexity.