The pursuit of scale in deep learning has entrenched a trade-off: computational throughput is prioritized at the expense of numerical precision. We argue this compromise is fundamentally at odds with the requirements of general intelligence. We propose the \textbf{Exactness Hypothesis}: high-order causal reasoning -- a cornerstone of AGI -- demands a substrate supporting \textbf{arbitrary-precision, logically consistent arithmetic}. We trace prevalent LLM failures, such as logical hallucinations and incoherence, to the inherent limitations of IEEE 754 floating-point arithmetic, where approximation errors compound catastrophically in deep functions. As a solution, we present the \textbf{Halo Architecture}, which transitions the computational foundation from approximate reals ($\mathbb{R}$) to exact rationals ($\mathbb{Q}$). Halo is realized through a custom \textbf{Exact Inference Unit (EIU)}, whose design -- featuring asynchronous MIMD reduction and dual-modular redundancy -- resolves the performance and reliability bottlenecks of exact computation at scale. In rigorous simulations, 600B-parameter BF16 models fail in chaotic systems within steps, while Halo sustains \textbf{perfect numerical fidelity} indefinitely. Our work posits exact arithmetic as non-negotiable for advancing reasoning-capable AGI and provides a co-designed hardware-software path toward verifiable, exascale-ready AI systems.

翻译：深度学习对规模的追求已固化了一种权衡：计算吞吐量被优先考虑，而数值精度则被牺牲。我们认为这种妥协从根本上与通用智能的要求相悖。我们提出**精确性假说**：高阶因果推理——AGI的基石——需要一个支持**任意精度、逻辑一致算术**的底层基础。我们将当前主流LLM的失败（如逻辑幻觉和前后矛盾）追溯至IEEE 754浮点运算的固有局限，其中近似误差在深层函数中会灾难性地累积。作为解决方案，我们提出**Halo架构**，该架构将计算基础从近似实数（$\mathbb{R}$）转变为精确有理数（$\mathbb{Q}$）。Halo通过定制的**精确推理单元（EIU）** 实现，其设计——采用异步MIMD规约和双模块冗余——解决了大规模精确计算的性能和可靠性瓶颈。在严格的模拟中，6000亿参数的BF16模型在混沌系统中几步内即告失败，而Halo能够**无限期地保持完美的数值保真度**。我们的工作主张精确算术是推进具备推理能力的AGI不可或缺的条件，并提供了一条软硬件协同设计的路径，以实现可验证的、面向百亿亿次计算规模的AI系统。