I figured those who dabble in math and physics on the side would find it interesting because while some of the maths are pretty heavy, the underlying concepts are not too terrible to grasp. After all, what is more rational than using math to prove from axioms that physical structure of the causal dimension and prove the existence of quantum or quasi-quantum mechanical action involved in causality?  If you can grasp the concept of vector interactions creating emergent tensor spacetime in order to instantiate a new reality. Because that is what causality is doing, causing a change in reality along the temporal axis. that change is a product (cross product if we're being technical). How and why this happens becomes much clearer once you understand qualitative primacy and how qualitative concept vectors interact with a specific count metric concept vector, you can quickly understand that derivatives are iterated multiples of t^-1 going on into infinity (which is also why any attempts at proving free will vs superdeterminism will be met with Goedel's laughing ghost.) But then I added fractional calculus to make the dimension continuous and proved causal memory, a phenomenon most commonly observed in viscoelastic materials.  

Oh and I'm honestly not sure how no one has realized this, but causal analysis is just vector calculus in a degenerate flattened subspace (because somehow integrating vectors and crossing them to create tensors in regression and other methods didn't make it obvious already?). Realizing this allows you to do fun things like solving Simpson's Paradox (Fubini's Theorem does wonderful things for unobserved variable detection if you use it as a null hypothesis instead of a law of calculus. if it is significantly different from zero, congrats you have a non-orthogonal variable messing with your data.) In the case of Simpson's Paradox, run the test on both levels, pick the one that does not fail, you have (m^n) -1 viable options where m is the number of integrations and n is the number of levels, and since only one options results in unusable signals, you get (m^n)-1. 

Also, not to sure what was "AI-ish" about my post last time, but unless we are arguing that AI is capable of deriving novel physical constructs from first principles and deductive reasoning, the abstract to my manuscript that I have submitted for peer review and which for some reason 65+ people have seen fit to download in the past 4 days on Zenodo and PsyArXiv (working on finding endorsements for arxiv), should end all AI related nonsense. If you think my claims are grandiose, wild, absurd, or whatever and that I am wrong, that is fine. I very well might be. Such is the nature of theoretical research, but there is a stark difference between wanting to be less wrong and being afraid to be wrong. So, my proof is linked, poke holes in it if you can.  Please. Because no idea is worth a damn until it has been stress tested.  

That's all I got. If ya got questions, please ask. Cause honestly, it'd probably be an interesting discussion. Especially to hear about what people might theorize or pontificate on about it. 

                                                                Abstract

This document presents a self-contained, field-theoretic framework in a generalized Lorentzian spacetime to formally unify a wide range of 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.

Keywords:
causal inference, field theory, Lorentzian geometry, derivative dimension, Born rule, hypertime, memory, geometric subsumption, qualitative primacy, hidden variables, Fubini's theorem, Bayesian inference, decision theory, machine learning, tensor calculus, manifolds, mathematical proof