Alignment Field Theory: A Geometric Formulation of AI Alignment as a Relational Vector Field

This paper presents a mathematical formulation of AI alignment as a measurable, geometric property over an N-dimensional cognitive-behavioral state space. Unlike scalar reward approaches (RLHF) or post-hoc classification (Constitutional AI), alignment in this framework is not a property of model output alone — it is a property of the relationship between output and a human reference. Alignment is decomposed into exactly three components that map word-for-word onto the standard definition: consistency with human values, intentions, and goals. Each component is independently measurable, correctable during generation, and learnable over time. This paper serves as the conceptual opening to Alignment Field Theory. It is not a proof — it is a framework.