From Fuzzy to Exact: The Halo Architecture for Infinite-Depth Reasoning via Rational Arithmetic

Abstract: Current paradigms in Deep Learning prioritize computational throughput over numerical precision, relying on the assumption that intelligence emerges from statistical correlation at scale. In this paper, we challenge this orthodoxy. We propose the Exactness Hypothesis: that General Intelligence (AGI), specifically high-order causal inference, requires a computational substrate capable of Arbitrary Precision Arithmetic. We argue that the "hallucinations" and logical incoherence seen in current LLMs are artifacts of IEEE 754 floating-point approximation errors accumulating over deep compositional functions. To mitigate this, we introduce the Halo Architecture, a paradigm shift to Rational Arithmetic ($\mathbb{Q}$) supported by a novel Exact Inference Unit (EIU). Empirical validation on the Huginn-0125 prototype demonstrates that while 600B-parameter scale BF16 baselines collapse in chaotic systems, Halo maintains zero numerical divergence indefinitely. This work establishes exact arithmetic as a prerequisite for reducing logical uncertainty in System 2 AGI.