High-Precision Measurement of the Hubble Constant and Resolution of Hubble Tension Based on the 11-Dimensional Volume Differentiation and Prime 11th-Order Difference Model

The precise measurement of the cosmic expansion rate (Hubble constant $$H_0$$) and the unification of physics are core research topics in the fields of current cosmology and physics. Since Hubble discovered the cosmic expansion, the measurement of the Hubble constant has always had irreconcilable deviations (Hubble tension) — the numerical values obtained by traditional observation methods (CMB observation, Cepheid variable observation, BAO observation) are significantly different. The core root lies in the fact that the traditional model is confined to the 4-dimensional spacetime framework, ignoring the high-dimensional effects and the underlying constraints of mathematical laws on cosmic evolution. At the same time, the mystery of the nature of dark matter and dark energy, and the disconnection between quantum mechanics and general relativity, further hinder human understanding of the ultimate laws of the universe. Existing high-dimensional theories (such as string theory) attempt to break through the limitations of 4-dimensional spacetime but fail to achieve precise quantification of high-dimensional effects and do not establish the intrinsic connection between mathematical laws and cosmic evolution. As the basic discrete law of the mathematical system, prime number laws have never been applied to the research of macroscopic cosmic evolution. To address the above dilemmas, this study proposes Shui's 11-Dimensional Volume Differentiation Theory and the Prime 11th-Order Difference Model, combining high-dimensional geometric evolution with prime number laws, achieving a subversive breakthrough in the theoretical system, accurately deriving the Hubble constant and completely resolving the Hubble tension, providing a new path for the unification of physics. This paper strictly follows Zenodo academic standards, elaborates on the research theory, derivation process, verification results and future prospects in detail, ensuring the repeatability, verifiability and academic rigor of the research.