Geometric Information Dynamics Construction A: Loop Quantum Gravity as an Information-Dynamical Reconstruction of SU(2) Representations

Based on two operational principles—Information Distinguishability Conservation and Finite Describability—this paper constructs a hierarchical dynamicalframework named ∞-Groupoid Cosmology. The core thesis of this framework isthat the causal closure of physical systems and the four-dimensional spacetimebackground are not a priori existent but emerge as a metastable state through afirst-order phase transition after the cumulative information kink crosses a criticalthreshold (Θc = Nc·ln2, Nc ≈ 83) in the underlying information dynamics. Withinthis self-consistent underlying logic, the core mathematical structures of Loop Quantum Gravity (LQG)—including the SU(2) gauge symmetry, spin network states,quantization of area operators, and the big bounce cosmological scenario—are rigorously reinterpreted and positioned as necessary manifestations of this informationdynamical framework under specific symmetry constraints. Theoretical derivationshows that elements in LQG typically regarded as a priori inputs or free parameters(such as the choice of the SU(2) group and the Immirzi parameter) are replacedby the rigidity of the underlying information geometry. This reversal of theoreticalhierarchy yields a series of unique and testable quantitative predictions, including a specific evolutionary index for the dark energy equation of state parameter(α = π/√3 ≈ 1.520), approximately 0.8% odd-mode-dominated oscillations in theamplitude of the primordial gravitational wave power spectrum, and a precise formula for black hole echo times, providing a new paradigm for testing quantumgravity theories with next-generation astronomical observations.