This paper develops an information-geometric perspective on holographic entropy based on the geometry of statistical distinguishability. Using Fisher information geometry, finite distinguishability resolution, and metric entropy, it derives bounds on distinguishable configurations and introduces a minimal distinguishability cut principle for operational entropy. When calibrated by gravitational thermodynamics, this principle reproduces the Ryu–Takayanagi form of holographic entanglement entropy, suggesting that holographic area laws arise from geometric constraints on distinguishability in state space.