In standard Euclidean mathematics, \pi is defined as a fixed dimensionless transcendental constant within an abstract flat axiomatic geometry; this definition remains entirely unaltered throughout this work. However, if physical spacetime possesses a discrete Planck-scale microstructure under quantum-gravitational effects, the physically measured circumference-to-diameter ratio need not coincide with the abstract \pi. This paper develops a self-consistent Three-Dimensional Time (3DT-LSF) framework, in which all spatial structures are emergent projections of three orthogonal fundamental time dimensions: quantum fluctuation time T_1, classical causal time T_2, and cosmic expansion time T_3. We introduce a scale-dependent dynamical scalar field \Pi(T_1,T_2,T_3) as the physical geometric observable, modeling macroscopic circular contours as statistical superpositions of discrete Planck-scale spacetime pixels. A unified first-order correction formula with strict dimensionless normalization is derived, together with theoretical deviation benchmarks intended for next-generation ultra-precision experiments. Crucially, this work rigorously distinguishes abstract mathematical constant \pi from spacetime-dependent physical observable \Pi, clarifying their categorical boundary. The scale-dependent evolution of \Pi serves as internal evidence for the core axiom of 3DT-LSF: fundamental time is primitive; spatial geometry is derivative.