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

In this proof, I extend and apply field-theoretic framework in a generalized (nD + T) spacetime, withsignature (−, +, ..., +), to formally subsume, reinterpret, and unify causal inference methods. I illustrate this unity by demonstrating its applicability to Difference-in-Differences (DiD), regression inter-action effects, potential outcomes, Dynamic Structural Equation Modeling (DSEM), and propensity scoring. Critically, I prove that Regression Discontinuity Design (RDD) and Regression KinkDesign (RKD) are field-theoretic boundary phenomena differentiated by the order of causal curvature discontinuity—interpretable as a collision angle within the manifold. This geometric-dynamicalparadigm offers a novel mechanism for the detection of unobserved variable bias, leveraging tensorcalculus and linear algebra. The framework’s predicted performance stems from its foundation inLorentzian spacetime, the inherent mathematical structure of causality, providing a native environment for causal relationships that is inaccessible to methods operating on degraded, flattened projections of reality. True mathematical discontinuities are shown to be approximations arising when thecharacteristic time scale of a causal transition falls below the observational time step, analogous tothe Planck time limit in physics. The empirical success of existing low-dimensional causal inferencemethods provide a compelling validation for the superior performance predicted out of mathematical necessity and of this higher-dimensional spacetime framework. NOTE: This is a first draft, expect errors and an additional section or two.