The prevailing scaling paradigm of Large Language Models (LLMs) rests on a substrate of "Fuzzy" floating-point arithmetic. To mitigate the inherent instability of this approximate foundation, modern architectures have erected a complex scaffolding of structural and numerical heuristics--Complex Residuals, Pre-RMSNorm, Attention Scaling, and Gradient Clipping--consuming significant compute solely to prevent numerical collapse. We propose a paradigm shift to the "Exact". We introduce the Halo Architecture, grounded in the Rational Field (Q) and powered by a custom Exact Inference Unit (EIU). To resolve the exponential bit-width growth of rational arithmetic, Halo employs a Dual-Ring Topology that unifies two complementary control mechanisms: (1) The Micro-Ring (Continuum Maintenance), which strictly bounds memory complexity via Diophantine Approximation; and (2) The Macro-Ring (Symbolic Alignment), which enforces logical consistency via periodic state collapse. This stable dual-ring substrate allows for the "Great Dismantling" of numerical scaffolding, reducing the Transformer block to its "Clean" algebraic form (Tabula Rasa). Furthermore, we verify the "Efficiency Paradox": the elimination of gradient noise (sigma -> 0) allows for Macro-Learning Rates, potentially reducing the Total Time-to-Convergence by orders of magnitude. Halo demonstrates that General Intelligence requires the hybridization of continuous fields and discrete chains under a rigorous mathematical framework.

翻译：当前大型语言模型（LLM）的扩展范式建立在“模糊”浮点算术的基底之上。为缓解这一近似基础固有的不稳定性，现代架构构建了由结构和数值启发式方法组成的复杂支撑体系——复杂残差、预RMSNorm、注意力缩放和梯度裁剪——消耗大量算力仅用于防止数值崩溃。我们提出向“精确”范式的转变，引入基于有理数域（Q）并由定制精确推理单元（EIU）驱动的光环架构。为解决有理数算术中指数级增长的位宽问题，光环架构采用双环拓扑结构，统一了两种互补的控制机制：（1）微观环（连续体维护），通过丢番图逼近严格约束内存复杂度；（2）宏观环（符号对齐），通过周期性状态坍缩强制逻辑一致性。这一稳定的双环基底实现了数值支撑体系的“大拆除”，将Transformer模块简化为其“纯净”的代数形式（白板状态）。此外，我们验证了“效率悖论”：梯度噪声的消除（σ→0）允许采用宏观学习率，可能将总收敛时间减少数个数量级。光环架构证明，通用智能需要在严谨数学框架下实现连续域与离散链的融合。