Causal Identifiability in High Dimensions: An Information-Orthogonality Framework

Modern AI systems excel at pattern recognition but suffer from causal blindness—relying on correlations rather than causal mechanisms—which undermines their reliability in high-stakes applications such as healthcare and autonomous systems. A foundational barrier is the lack of a universal framework for causal direction identifiability (\(X \to Y\) vs. \(Y \to X\)) that is compatible with high-dimensional inputs, non-linear mappings, and black-box architectures. This paper establishes the first rigorous, assumption-light, distribution-free theory of causal identifiability for arbitrary multivariate systems, grounded in two core principles: Causal Information Orthogonality (CIO) and the Dimensional Constraint Principle (DCP). We prove three fundamental theorems: (1) a necessary and sufficient condition for identifiability that requires no restrictive distributional assumptions and scales to high-dimensional data; (2) the equivalence between information-theoretic orthogonality and geometric dimensional separation, providing an interpretable basis for integrating causality into black-box models; (3) a strict robustness boundary showing identifiability is stable under bounded perturbations (e.g., measurement noise, distribution shift). Our results unify fragmented causal inference methods and provide a first-principles foundation for causal AI, enabling systems to move beyond correlational learning to actionable causal reasoning. The theory is non-asymptotic, requires minimal regularity, and is directly applicable to high-dimensional AI domains such as computer vision, NLP, and medical AI.