Within the framework of the "Topological Residual Fundamental Entropy Increase Theory,"physical constants and fundamental phenomena are reinterpreted as products of the cobootstrapping between the cosmic residual network and the observer's cognitive residuals. The three-layer π-topological geometric expansion defines the geometric origin of the finestructure 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 φu207b². 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 tubetopological defects, strictly confined under the protection of three-layer topology and sixdegree separation [4,5]. Simultaneously, Planck's constant is revealed as the "cosmic pixellimit" after residual exhaustion, while ln(10) serves as the final seal of the initiator's basecognitive residual. Dimensional self-consistency is achieved by introducing Factor_h as abridge from geometric topology to electromagnetic dimensions. This paper systematically presents the mathematical self-consistency, structural inevitability, and philosophical depth of the theory.