Topological Residual Fundamental Entropy Increase Theory: Geometric Origin of Constants, Error Analysis, Black Hole and Magnetic Monopole Resolution

Published May 13, 2026 | Version v1

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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

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