Within the framework of the "Topological Residual Fundamental Entropy Increase Theory," physical constants and fundamental phenomena are reinterpreted as products of the co bootstrapping between the cosmic residual network and the observer's cognitive residuals. The three-layer π-topological geometric expansion defines the geometric origin of the fine structure constant α_geom ≈ 1/137.036, with its theoretical foundation rooted in the pure geometric universe framework that establishes "spatial right-handed cylindrical helical light-speed motion" as the sole first-principle axiom [1,2]. This further yields theoretical values for the gravitational constant G_theory and Planck's constant h_theory, with relative experimental residuals of approximately 0.261193% and 0.54256%, respectively. These residuals are structurally closed through the affine renormalization mapping involving the Fibonacci critical node 4181 and the golden ratio conjugate square φ⁻². The black hole information paradox and the missing magnetic monopole problem are topologically resolved within this framework: the black hole horizon is a macroscopic condensation of extreme residual networks, with information preserved through the six-degree separation network [3] and the observer closed loop; magnetic monopoles are bare magnetic tube topological defects, strictly confined under the protection of three-layer topology and six degree separation [4,5]. Simultaneously, Planck's constant is revealed as the "cosmic pixel limit" after residual exhaustion, while ln(10) serves as the final seal of the initiator's base cognitive residual. Dimensional self-consistency is achieved by introducing Factor_h as a bridge from geometric topology to electromagnetic dimensions. This paper systematically presents the mathematical self-consistency, structural inevitability, and philosophical depth of the theory