Z-Geometric Dynamics II: Geometric Entropy and the Limiting Structure of the Universe

In the ZGD framework (Paper I) 1, 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, we introduce an axiom of conservation of total information capacity, together with an initial condition axiom (the initial cosmic scale equals its equivalent Schwarzschild radius) and the maximum entropy hypothesis, to define a new fundamental constant—the geometric entropy constant α. This constant is related to the initial horizon Rᵢ of the information universe by α = 1/π(Rᵢ/lₚ)². By comparing the total information capacity of the information universe with that of the currently observable universe, we derive the inequality α ≤ 1/ln(Rₚ(0)/lₚ) ≈ 0.007067, thereby excluding the fine-structure constant αₑₘ as a candidate for α. The paper also presents a physical picture of "spatial thickness" to motivate the correction factor in the five-dimensional topological excision model of Paper III. The conservation of information directly leads to a geometric resolution of the black hole information paradox. This work lays a self-consistent foundation of constants for the unification of forces (Paper III) and for cosmic evolution (Paper IV, future work).