Z-Geometric Dynamics II: Geometric Entropy and the Information Universe

In the ZGD framework (Paper I), the particle horizon Z with radius Rp (0) =4. 4×10²6 m is used to explain galactic-scale dark matter phenomena. This paper further explores the origin of this horizon. Starting from quantum mechanical unitarity, this paper introduces an axiom of conservation of total information capacity, together with an initial condition axiom and the maximum entropy hypothesis, to define a new fundamental constant—the geometric entropy constant α=1/π (Ri/lP) ². By analyzing the geometric path of the observer’s information reception, a universal upper bound Iobs ≤ Sinfo=1/α is established, and the convergence of the conformal path integral rigorously proves that the current universe is extremely close to this bound (information entropy gap of only about 0. 011). This paper proposes a physical picture of “spatial thickness, ” distinguishing the fine-structure constant as an internal property constant from the geometric entropy constant as a global structure constant, and on this basis conjectures αEM=32/31 α. The axiom of information conservation directly leads to a geometric resolution of the black hole information paradox. This work provides both a numerical anchor and intuitive motivation for the subsequent unification of forces (Paper III).