Derivation of Generalized Uncertainty Principle from Noncommutative Geometry of κglobal-Network

This paper presents a rigorous derivation of the Generalized Uncertainty Prin ciple (GUP) based on the noncommutative geometric structure of the κglobal-qubit network in κglobal-quantum gravity theory. By establishing the C*-algebra formula tion of the κglobal-network, we define position and momentum operators as quantum information flow operators, whose noncommutative relations naturally arise from the topological constraints and renormalization group invariance of the network. The derivation reveals that the GUP contains a correction term proportional to κ −1 / 3 global: ∆x∆p ≥ ℏ/2 + β0(ℓ 2 P /ℏ)κ − global 1/3 (∆p) 2 , where β0 ≈ 0.24 is a constant deter mined by the topological invariants of the Chern-Simons action. This result unifies quantum mechanics with gravitational effects and can be verified through tabletop experiments such as LIGO ringdown analysis and quantum processor error thresh old measurements. This work establishes for the first time a quantitative connection between the Generalized Uncertainty Principle and the information capacity of the universe within the framework of quantum information ontology.