Natural Orthogonality Between Semantic and Spatial Structure: Evidence from Large-Scale Null-Correlation Studies

Abstract Semantic–Spatial Correlation (SSC) quantifies the alignment between semantic structure and spatial organization.Although SSC is widely used in cognitive science, neuroscience, and AI, its natural baseline—what SSC should be under semantic–spatial independence—has never been systematically characterized.This study provides the first large-scale empirical demonstration of natural orthogonality: under value-free conditions (λ=0\lambda = 0λ=0), SSC converges to a near-zero distribution across diverse semantic embeddings, distance metrics, spatial layouts, and sample sizes. Across 1,000 trials per condition with independent semantic and spatial generation, SSC follows a tightly concentrated null distribution centered at zero, with 90% CIs fully contained within the quasi-orthogonal region (∣SSC∣≤0.01).Multilingual validation using pretrained BERT models (English, Japanese, Chinese) confirms that natural orthogonality generalizes to real-world linguistic representations.A mechanistic explanation integrating high-dimensional geometry, statistical independence, and neural representational structure accounts for this phenomenon. Natural orthogonality provides a principled baseline for evaluating when structure–meaning alignment is meaningfully above chance, forming the observational foundation for value-gated coupling and the broader Relativity of Intelligence framework.All code, data, and figure source files are archived as a version-frozen reproducibility bundle.