A prevailing assumption in machine learning is that model correctness must be enforced after the fact. We observe that the properties determining whether an AI model is numerically stable, computationally correct, or consistent with a physical domain do not necessarily demand post hoc enforcement. They can be verified at design time, before training begins, at marginal computational cost, with particular relevance to models deployed in high-leverage decision support and scientifically constrained settings. These properties share a specific algebraic structure: they are expressible as constraints over finitely generated abelian groups $\mathbb{Z}^n$, where inference is decidable in polynomial time and the principal type is unique. A framework built on this observation composes three prior results (arXiv:2603.16437, arXiv:2603.17627, arXiv:2603.18104): a dimensional type system carrying arbitrary annotations as persistent codata through model elaboration; a program hypergraph that infers Clifford algebra grade and derives geometric product sparsity from type signatures alone; and an adaptive domain model architecture preserving both invariants through training via forward-mode coeffect analysis and exact posit accumulation. We believe this composition yields a novel information-theoretic result: Hindley-Milner unification over abelian groups computes the maximum a posteriori hypothesis under a computable restriction of Solomonoff's universal prior, placing the framework's type inference on the same formal ground as universal induction. We compare four contemporary approaches to AI reliability and show that each imposes overhead that can compound across deployments, layers, and inference requests. This framework eliminates that overhead by construction.

翻译：机器学习领域的一个普遍假设是模型正确性必须在事后强制实现。我们观察到，决定AI模型是否具备数值稳定性、计算正确性或与物理领域一致性的属性并不一定需要事后验证。这些属性可以在训练开始前的设计时以极低计算成本进行验证，尤其适用于部署在高风险决策支持及科学约束环境中的模型。这些属性共享特定的代数结构：它们可表达为有限生成阿贝尔群$\mathbb{Z}^n$上的约束条件，其中推理过程可在多项式时间内判定，且主类型唯一。基于该观察构建的框架整合了三项先前成果（arXiv:2603.16437、arXiv:2603.17627、arXiv:2603.18104）：一个维度类型系统，通过模型精化将任意标注作为持久共数据传递；一个程序超图，仅从类型签名推断克利福德代数阶数并导出几何积稀疏性；以及一种自适应领域模型架构，通过前向模式余效应分析和精确正数累加在训练过程中保持两个不变量。我们认为这种整合产生了新颖的信息论结果：阿贝尔群上的Hindley-Milner类型化可在所罗门诺夫通用先验的可计算限制下计算最大后验假设，使该框架的类型推理与通用归纳法具有相同的形式基础。我们比较了四种当代AI可靠性方法，并表明每种方法都会产生跨部署、跨层级及跨推理请求累积的开销。本框架通过构造性设计消除了这些开销。