Prime Space Cluster Hypothesis: A New Path to Cosmic Symmetry and Conservation (Abridged Academic Version)

This paper proposes the Prime Space Cluster Hypothesis, which treats the prime number sequence as the underlying discrete structure of cosmic spacetime. By defining the prime space and prime clusters, a unified framework of number theory, high-energy physics and cosmology is constructed. The hypothesis is based on three fundamental assumptions: primes are the intrinsic markers of spacetime discretization, prime clusters correspond to the topological structure of cosmic symmetry breaking and conservation, and the evolution equation of prime space is equivalent to the dynamical equation of cosmic spacetime. The core contributions include: 1. Defining the prime space P and prime clusters Cₙ, and establishing their topological conservation relations; 2. Deriving the symmetry conservation equation of prime clusters ₏ ₂䂸 1p 1 2, which is isomorphic to core laws such as cosmic energy conservation and charge conservation; 3. Proposing three testable predictions: the correlation between dark matter distribution and prime cluster density, the evolution of strong interaction coupling constant and the power-law relationship of prime spacing, and the distribution of prime pairs corresponding to high-dimensional compactification structures. This hypothesis provides a quantifiable topological path for "the unity of mathematics and physics" and a new number-theoretic perspective for the underlying origin of cosmic symmetry conservation.