The N-Universe A Mathematical Framework for the Representation of Human Abstracts in AI Systems

Abstract

Contemporary artificial intelligence systems demonstrate remarkable capacity for pattern recognition and statistical inference; however, an explicit internal structure for representing human abstract concepts such as power, love, trust, and freedom remains absent. These notions are typically treated as qualitative or context dependent constructs, without a formal relational architecture that enables structural interpretation, manipulation, and dynamic simulation. The N-Universe is introduced as a mathematical and geometric framework designed to represent human abstracts as structured relational entities within a unified formal space. The framework is grounded on the structural principle that each human abstract possesses an intrinsic geometry, understood as a characteristic relational organization that can be formally described through distinct geometric structures. Such geometries are not metaphorical illustrations, but mathematically defined configurations expressing essential properties including orientation, distribution, symmetry, intensity, and dynamic variation. Whereas Gärdenfors' conceptual spaces employ geometry in a static sense, as a similarity metric organizing categorization within a single cognitive agent, the N-Universe employs geometry in a dynamic sense, describing how an abstract behaves, propagates, and reacts over time within a bounded social-relational environment N composed of interacting human agents. The shared vocabulary of "intrinsic geometry" should not obscure this fundamental difference in what is being modeled: a static representational structure versus a dynamic relational process. Within this setting, abstract concepts are modeled as geometric configurations defined over a relational domain in which vectors, fields, and gradients encode structural properties. Power is formally defined as a vector structure possessing magnitude, vertical direction, and orientation determined by the interaction between applied power and reactive power. This formulation allows power to be interpreted as an oriented relational magnitude whose dynamics arise from the interplay between deliberate action and structural response of the environment. Love may be conceived, under the intrinsic geometry principle proposed by the N-Universe, as a radial field centered on a relational nucleus, with intensity decreasing as structural distance increases, thereby expressing cohesion and affective attraction. In a similar manner, trust may be interpreted as a continuous structural gradient describing stability and directional coherence across agents along relational or temporal axes. These formulations indicate potential geometric extensions of the framework rather than fully formalized components of the present model. Formally, a structured relational space is defined in which abstract fields are measurable, dynamically evolving, and computationally tractable. Symbolic interpretation is integrated with continuous mathematical representation, enabling hybrid reasoning and structured semantic analysis. By transforming qualitative human abstracts into geometrically intrinsic and mathematically coherent relational objects, a foundation is established for interpretable abstraction modeling, social simulation, and structurally grounded artificial intelligence systems.