Unified Causal Field Theory: A Proof of Geometric Subsumption and Extension of Causal Inference Methods Into Unified Framework

This document presents a self-contained, field-theoretic framework in a generalized nD+T Pseudo-Riemannian spacetime (-,+,+,...,+) to formally unify causal inference methods. I prove that established methods are geometric projections of this underlying reality. A key result is the formalization of Hypertime, a `derivative dimension` that models the interaction between spatial concepts and temporal dynamics. Within this causal tensor spacetime, I propose a new `Born Rule` for the emergence of causation from the interaction of vector-like states. This geometric-dynamical paradigm offers a novel mechanism for the detection of unobserved variable bias using operator non-commutativity and provides a mathematical origin for memory effects via the sinusoidal structure of fractional derivatives. The framework extends beyond traditional causal inference to encompass Bayesian statistics (belief updates as field dynamics), decision-making processes (softmax-to-argmax transitions as causal collapse), machine learning (parameter evolution as causal geodesics), and multi-agent systems (strategic interactions as causal field evolution) as manifestations of causal field theory. The empirical success of existing low-dimensional causal inference methods provides a compelling validation for the mathematical necessity and superior performance of this higher-dimensional spacetime framework. This proof serves as both a standalone treatise and the foundational pillar for a broader monograph on Unified Cognitive Field Theory.