Space Quantum Topological Emergence Theory (SQTE) - Unified Construction from Galois Symmetry to the Physical Universe

Space Quantum Topological Emergence Theory (SQTE) takes Space Quantum Nodes (SQN) as the sole fundamental substance and constructs a global geometric invariant triple composed of holographic active density ρ, topological coupling coefficient ξ, and topological stability scalar φ. It also introduces the quadratic field extension Q (φ) and its Galois symmetry group GGal=Gal (Q (φ) /Q) ≅Z₂ as the underlying algebraic foundation, replacing the conventional lattice and space group descriptions to endow the theory with a more rigorous mathematical basis. Within this framework, intrinsic–virtual two-layer topology and symmetric constraint potentials emerge naturally. The intrinsic difference in Galois conjugate symmetry gives rise to a topological energy gap at the electroweak scale, providing a microscopic topological origin for the Higgs mechanism and electroweak symmetry breaking. The topological shielding and topological protection effects can be utilized for the principle verification of topological qubits. At high energy scales, the theory yields falsifiable predictions at the Planck scale (e. g. , Lorentz violation and gravitational wave frequency shifts) ; in the low-energy limit, it recovers the Standard Model and quantum field theory. On macroscopic scales, gravity and corrections to galactic rotation curves (replacing dark matter) are naturally derived from topological gradients. In cosmology, it offers a unified explanation for the Hubble gradient tension, suppressed primordial gravitational waves, and large-scale fractal structures. Through topological duality invariance and Cantor-type fractal spectra, SQTE achieves mathematical isomorphism with global theory, quasi-periodic dynamics, and the Hofstadter butterfly spectrum. The entire framework discards ad-hoc assumptions such as extra dimensions, dark matter, and dark energy, and achieves a unified description of spacetime, quantum phenomena, gravity, and matter with a minimal set of substances and axiomatic structures. The theory possesses inherent advantages in graph computation and symmetry reduction, enabling exact solutions with linear complexity via the Galois group Z₂ and graph neural networks (GNNs). This provides a unified, efficient, and scalable first-principles computational framework for research fields including black hole physics and molecular design.