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

I follow the foundational scientific method of using a formal proof to mathematically derive from first principles, relying on no external justification, proof that causality follows field theoretic principles. And in following this standard practice from pure and theoretical science, I start from axioms such as the applicability of generalized (nD + T) spacetime, with signature (−, +, ..., +), to formally subsume, reinterpret, and unify causal inference methods. I illustrate this unity by demonstrating its applicability to Difference-in-Differences (DiD), regression interaction effects, potential outcomes, Dynamic Structural Equation Modeling (DSEM), and propensity scoring. Critically, I prove that Regression Discontinuity Design (RDD) and Regression Kink Design (RKD) are field-theoretic boundary phenomena differentiated by the order of causal curvature discontinuity—interpretable as a collision angle within the manifold. This geometric-dynamical paradigm offers a novel mechanism for the detection of unobserved variable bias, leveraging tensor calculus and linear algebra. The framework’s predicted performance stems from its foundation in Lorentzian 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 the characteristic time scale of a causal transition falls below the observational time step, analogous to the Planck time limit in physics. The empirical success of existing low-dimensional causal inference methods provides 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. (To the mod who rejected this and said this is not science, this is theoretical physics, but because, as I prove, physics is the science of causality (it just focuses on the ground state of the universe; matter, energy, and time), this proof, if validated by peers, has the potential to revolutionize the ENTIRETY OF QUANTITATIVE SCIENCE. Now I may be wrong on this proof in every single way; I’m not, at least not all.. Nevertheless, I if I am, so be it; such is the nature of theoretical science. But, I know this much for certain, people who do not know what theoretical science is or looks like should not be gatekeeping OPEN SCIENCE anymore than someone who can’t recognize a heart should be a cardio surgeon. If you think my claim unbelievable that is fine, take my work scrutinize it, and prove me wrong or don’t. As I said, maybe I am. But without the very scientific method used here in this paper there would be no relativity (Newtonian, general, or special), no information theory, no genetics, no quantum mechanics, no internet search engine, no AI, none of it. The lack of citations is not a bug, it is literally the point. The landmark papers from Einstein, Schrödinger, Gödel, Dirac, Hawking, Shannon, collectively had 0 citations. Simply put, this is the scientific methodology from which all other methods are born. If if it the policy of OSF is to prohibit the foundational methodology of science itself, they have an ethical obligation to state as much as official policy. This proof will either stand and speak for itself or it will crash and burn like Icarus. But here’s the reality, science demands that we allow good faith efforts to fail if that is their fate; to do anything else would be to stifle innovation and discovery. So I ask, are we here for open science or echo chambers?