bstract 1 Core Research Pain Points: In the interdisciplinary field of number theory and quantum field theory, there exists a long-standing core logical barrier rooted in the widespread conceptual confusion between the intrinsic topological structural properties of spacetime and artificial numerical observation truncation. At this stage of research, the mathematical correlation mechanism between finite observation precision and prime periodic modulus systems has not been established, resulting in all numerical precision truncation rules relying merely on engineering experience and lacking fundamental number-theoretic theoretical support. Traditional mathematical frameworks conflate the inherent geometric dimensional attributes of manifolds with the technical constraints of finite computing power and finite observation, which indirectly induces a series of theoretical dilemmas including numerical divergence, incomplete description of global information conservation, and ambiguous analytical boundaries between classical observable systems and quantum transcendental systems. 2 Core Research Ideas: To resolve the above theoretical contradictions, this paper first constructs a double-layer independent theoretical framework to strictly separate the intrinsic topological rules of the universe from the artificial constrained numerical observation rules. Based on a customized symmetric dichotomy fundamental hypothesis, a 64-dimensional smooth manifold model composed of a 32-dimensional real topological subspace and a 32-dimensional imaginary topological subspace is established as the fundamental mathematical substrate connecting global spacetime geometry, analytic number theory, and transcendental field theory, realizing the hierarchical decoupling of intrinsic geometric laws and observational numerical laws. 3 Key Innovative Mechanisms: This paper innovatively introduces a progressive nested prime periodic modulus system including modulo 30, modulo 210, and modulo 30030 and attempts to interpret the fundamental number-theoretic logic of the rigid truncation of 16 significant decimal digits. Under the framework of this model, the 16 significant digit interval corresponds to the periodic regular convergence interval of the real domain, while the high-order numerical values beyond 16 digits correspond to the quantum transcendental divergence interval of the imaginary space, providing a new perspective for explaining the mathematical origin of precision truncation boundaries. The 16-digit rigid numerical truncation rule constructed based on this prime periodic system only constrains numerical operation and observation fitting in the real topological domain, which can effectively match the finite observation characteristics of macroscopic spacetime, suppress numerical divergence in the real domain, and completely retain the infinite analytic continuation characteristics of the 32-dimensional imaginary topological space. 4 Research Value and Paradigm Breakthrough: Thedifferentiated logic of virtual-real dimensional precision and hierarchical prime periodic modulus system provides a novel mathematical model for the self-consistent connection between classical finite observational spacetime and quantum infinite transcendental fields. Different from the engineering definition of traditional computer binary bit width, the topology-number theory-precision double-layer coupling framework constructed in this paper avoids the logical loopholes of mixing dimensional proportioning and numerical constraints, and can provide self-consistent model preconditions for holographic projection reversibility, Riemann zeta function zero-point analysis, and global information conservation, establishing an original interdisciplinary research paradigm for the mathematical integration of macroscopic classical physics and microscopic quantum theory.
xiaogang shui (Mon,) studied this question.