On the Four-Dimensional Spacetime Symmetry Conjecture of α = sin(3π/8) in Memory Force Theory

Without introducing extra dimensions or modifying the classical limit of general relativity, this paper proposes a core geometric conjecture based on the self-consistency of the seven perspectives of memory force theory and the multifractal structure of the QCD vacuum in lattice QCD. The key parameter α = sin(3π/8) is identified as an intrinsic geometric characteristic constant of the four-dimensional spacetime symmetry described by the octahedral dihedral group D₈. It is shown that four-dimensional spacetime behaves as an isotropic Lorentzian manifold at classical scales, while exhibiting discrete D₈ symmetry at quantum and vacuum lattice scales. A pair of infrared-ultraviolet dual constants sin(π/8) and sin(3π/8) arise, satisfying the normalization relation sin²(π/8) + sin²(3π/8) = 1. A three-dimensional observer, as a three-dimensional submanifold embedded in four-dimensional spacetime, has its perceptual boundary determined by the coupling constant sin(3π/8). The "three-dimensional confinement" is not an external constraint but the intrinsic geometric identity of the observer. This paper provides two quantitatively testable predictions in lattice QCD: multifractal dual peaks and anomalous scaling of correlation functions, offering a new theoretical approach to the quantum geometric structure of four-dimensional spacetime.