Finite-Information Universe\\ and Parameter Vector \Theta:\\ Entropy Bounds, Axiomatization\\ and Quantum Cellular Automaton Source Code Length

Standard picture of continuous spacetime and quantum field theory suggests: mathematically specifying a complete ``universe'' object seems to require infinitely much information---infinitely many spacetime points, infinitely many degrees of freedom at each point, initial conditions as infinite-precision real-valued functions. This ``infinite-information universe'' picture faces fundamental difficulties both physically and information-theoretically. On other hand, black hole entropy bounds, holographic entropy bounds and quantum computation limits jointly strongly suggest: within finite energy and finite spacetime region, physically distinguishable information amount has finite upper bound. Building on solid foundation given by Bekenstein entropy bound, Bousso holographic bound and Lloyd computation limit, this paper introduces ``finite information capacity'' axiom: exists finite constant I_{\max} < \infty such that physically distinguishable total information amount of entire observable universe does not exceed I_{\max}. Under this axiom, we prove: ``universe'' can be viewed as object completely specified by finite bit string \Theta, give systematic parameter vector decomposition $ \Theta = (\Theta_{str},\Theta_{dyn},\Theta_{ini}), respectively describing spacetime/lattice/topological structure, quantum cellular automaton (QCA) dynamics rules and initial quantum state. In concrete Dirac-type QCA universe model, we constructively give information complexity upper bound: under strong translation symmetry, fixed gate set and finite-precision discretization assumptions, encoding lengths of structural parameters, dynamical parameters, initial state parameters can be controlled at order O(10^2), O(10^3), O(10^2--10^3) bits respectively, thus obtaining typical source code information amount estimate I_{param}(\Theta) = |\Theta_{str}| + |\Theta_{dyn}| + |\Theta_{ini}| \sim 10^3 bits, far smaller than maximum entropy S_{\max}(\Theta) \sim 10^{90--122} bits estimated from universe horizon area. We further prove information--entropy inequality I_{param}(\Theta) + S_{\max}(\Theta) \le I_{\max}, showing ``small source code'' and ``giant entropy universe'' compatible under finite information capacity axiom. To address intuitive question ``why can extremely small initial data evolve into extremely high complexity universe'', this paper analyzes evolutionary structure of QCA universe from dynamical system and quantum superposition perspective: given short parameter vector \Theta, entire universe history viewable as finite program linear unitary evolution in high-dimensional Hilbert combinatorial space; quantum superposition is not ``brute force enumeration of all permutation combinations'', but realizes amplitude and phase unified update and interference on ``linear envelope of all classical combinations''. This explains why ``source code universe'' with finite algorithmic complexity can macroscopically present complex structure approaching maximum entropy. Finally, we discuss structure on parameter space M_\Theta, finite information inequality constraints on lattice number and unit Hilbert dimension, and how anthropic principle and physical constraints compress possible universe set to extremely small realizable subset under given finite I_{\max} and parameter vector \Theta$.