This paper introduces Geometric Context Modeling as a new field of inquiry and a new class of artificial intelligence systems. Current AI systems are built on one of two foundations: statistical language modeling, which represents meaning as probability distributions over token sequences; or symbolic knowledge representation, which encodes meaning as discrete facts and rules. Neither approach maintains a continuous, explicit, geometric representation of where a conversation is in semantic space.Geometric Context Modeling proposes a third foundation. Meaning is encoded as position in a structured geometric space with defined axes, distances, and directions. Context is maintained as a trajectory through that space, updated continuously by each new input using a fixed-size state vector. Routing and reasoning operate through geometric operations: projection, nearest-neighbor lookup, weighted combination, and directional navigation. No token prediction is required. No discrete symbolic facts are required. Geometry is the representation.We document the theoretical basis for this paradigm, survey the existing work that approaches it without fully committing to it, identify the precise gap between that work and what Geometric Context Modeling proposes, and introduce KAIA (Knowledge Architecture for Intelligent Agents) as the first implemented system in this class. KAIA maintains a 52-byte context state regardless of conversation length, operates at 44,000 to 97,000 tokens per second on a standard CPU with no GPU requirement, and achieves 70 to 85 percent accuracy across a seven-benchmark suite of agent-oriented semantic reasoning tasks.
Tiffney Bare (2026) studied this question.