P-0: The Language of Space — The Spatial Orientation Field Equation and Its Physical Significance

What is space? What is matter? What is interaction? What is the quantum? This paper provides a unified answer to these four fundamental questions from a novel first principle—Space Ontology. Space is the sole entity. Matter is a localized motion pattern of space, self-organized under the drive of energy-momentum via nonlinear dynamics. Interactions are the geometric couplings of different motion patterns through their shared spatial background. Quantum phenomena are the intrinsic statistical behaviors of this classical nonlinear system under topological constraints. These four statements are condensed into a single equation: ∂_μ ∂^μ n + λ (n·n − 1) n + κ (∂_μ n × ∂^μ n) = 0 This is the language of space. This paper rigorously derives this equation from first principles and systematically expounds its mathematical structure, physical significance, and key properties—Lorentz covariance, topological quantization, and the existence of soliton solutions. We prove that the strong interaction is the collective condensation of topological defects of this equation, the electromagnetic interaction is the linearization of small perturbations, the weak interaction is the chiral symmetry breaking of a complexified field, and the gravitational interaction is the identification of the κ term with spacetime torsion. The four fundamental forces are different facets of the same geometric entity. The equation's sole free parameter, κ = 0.017, has been cross-determined through five independent physical domains: nuclear force, electroweak unification, and cosmology. κ is the "torsional stiffness" of space. If κ = 0, space cannot form vortices, and the universe would have only waves (light), no particles. If κ ≫ 1, space is densely packed with particles, leaving no vacuum and no structure. κ = 0.017 is the "just right" number that explains why we exist. This paper is the zeroth paper of the Space Ontology series (the first series, Foundational Theory), establishing the theoretical cornerstone upon which all subsequent work in the series is built.