A Unified Cross-Scale Physical Theory Based on Discrete Spacetime and Spiral Motion (V4.0)

Note: The mass difference of the fourth-generation fermion between the two versions (~8.4 GeV/c² in v3.3/v3.3.1 and ~862 GeV/c² in v4.1) stems from an essential distinction in physical definitions: the former refers to the intrinsic rest mass of the particle (consistent with the mass definition of fermions in the Standard Model), while the latter denotes the "resonant equivalent mass" formed by the particle in the energy fiber network (with the introduction of the network resonance amplification factor ξ). Both versions feature self-consistent core derivation logic without theoretical errors. Abstract: This study presents a groundbreaking unified framework that bridges the profound gap between quantum and classical physics. Departing from conventional approaches, we propose a core principle: the universe's fundamental operations manifest as helical motions within a discrete energy-fiber network, governed by modulo-9 congruence number theory. Our theory's power lies in its "Trinity" formula system, which seamlessly integrates three distinct yet interconnected governing equations for subatomic particles, atoms/molecules, and macroscopic systems. This framework is rigorously validated against a vast dataset of 1,034 cross-scale samples—from electrons and nucleons to atoms, nanomaterials, and celestial bodies—achieving a remarkable average relative error of just 1.18%. Key to its practicality, we provide fully reproducible Python code that delivers these results with a single click. The theory makes two bold and falsifiable predictions: It predicts a fourth-generation fermion with a resonant equivalent mass of 862 GeV, a clear target for future collider experiments. It accurately forecasts the characteristic frequency of a 15nm gold nanoparticle at 4.34×10¹³ Hz, which aligns with independent experimental measurements. For researchers in quantum materials and quantum technology, this work offers a novel perspective. By providing a unified descriptor for properties from the atomic scale upward, it opens new avenues for predicting the emergent behavior of complex quantum systems and designing materials with tailored functionalities. This work challenges scale-fragmented paradigms and provides a computationally transparent, testable tool for unified physical modeling.