Space Quantum Topological Emergence Theory (SQTE) - Ontological Reconstruction Based on the Galois-Physical Duality Program

This work is based on the framework of Space Quantum Topological Emergence Theory (SQTE), adhering to the core principle: *Space as foundation, quantum as basis, topology as structure, emergence as principle*. It aims to establish a unified theory of quantum gravity that is logically consistent, mathematically rigorous, and physically complete, while deeply integrating frontiers in modern mathematics, high-energy physics, cosmology, and quantum information. For a long time, the apparent conflict between general relativity and quantum mechanics, the Hubble tension, the hierarchy problem, and the dilemmas of dark matter and dark energy are essentially macroscopic illusions arising from the mismatch between the continuous spacetime hypothesis and the underlying discrete quantum Space ontology. The fundamental laws of the physical world are not governed by perturbation expansions, ad hoc assumptions, or extra dimensions, but by geometric invariance, topological stability, and fractal self-consistency. To this end, the theory accomplishes four foundational reconstructions: ontological reconstruction, mathematical foundation, physical mechanism, and the Galois–Physical Duality Program. This program establishes a strict mapping dictionary from algebraic geometry to physical reality: the arithmetic structure of the field extension Q(φ) (Galois group, ideal class group) is directly dually mapped to the material structure of the physical world (particle spectrum, dark charge, topological defect). This program is not merely a mathematical isomorphism, but also a generator of physical laws—it liberates the spirit of Langlands from pure mathematics, making it the ultimate meta-code driving cosmic evolution and governing light-dark interactions. Within this framework:- Microscopic level: The topological screening effect naturally resolves the hierarchy problem of the Standard Model; the topological protection effect provides a theoretical basis for stable particles, superconductivity, and topological quantum computation.- Macroscopic level: The Topological Renormalization Group Flow (TRG) transforms scale evolution into the geometric phase transition of discrete Space → continuous spacetime, achieving full-scale coherence from the Planck scale to low-energy physics. SQTE relies on Z₂ Galois symmetry and is naturally compatible with graph neural networks, achieving mathematical isomorphism with quasiperiodic dynamics, Hofstadter butterfly, and global theory. It presupposes no external conditions, requires no initial creation, and depends on no external tuning. With unique ontology, minimal axioms, global invariance, and topological emergence, it achieves a unified description of spacetime, quantum, gravity, matter, dark universe, and quantum information, marking a paradigm shift in physics from continuous geometry to discrete quantum topological emergence.