The concept of faster-than-light (FTL) motion challenges our fun- damental understanding of causality and relativity. This paper ex- plores a phenomenological model for velocity computation, examining the dependence of normalized velocity v/c on parameters such as the effective coupling Γx, the angle β, and terms incorporating lα and Θr. Multiple parameter configurations are investigated through numerical simulation to identify cases where velocities approach or exceed c, the speed of light. Key trends and observations are highlighted, providing a framework for future (...) theoretical work. (shrink)

In this paper, we extend the mathematical framework of **non-commutative scalar fields** and numerical techniques discussed previously to build a foundation for **AI-based reasoning systems**. The goal is to enable AI to operate over **symbolic hierarchies, semantic transformations**, and **large-scale infinite or non-commutative domains**. Inspired by quantum tensor field operations, we integrate reasoning over symbolic, numeric, and approximate representations into machine learning pipelines. This work leverages concepts from numerical techniques for non-commutative mixed derivatives, recur- sive tensor calculus, and symbolic transformation (...) logic to build **deep learning architectures** capable of representing and reasoning with structured, hierarchical complexity. (shrink)