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：机器学习中普遍假设模型的正确性必须在事后强制实现。我们观察到，决定AI模型是否数值稳定、计算正确或与物理领域一致的属性，并不一定需要事后强制执行。这些属性可以在训练开始前的设计时，以极小的计算成本进行验证，尤其适用于部署在高风险决策支持和科学约束场景中的模型。这些属性共享特定的代数结构：它们可以表示为有限生成阿贝尔群 $\mathbb{Z}^n$ 上的约束，其中推理在多项式时间内可判定且主类型唯一。基于这一观察的框架整合了三项前期研究（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注解作为持久协数据传递；一个程序超图，仅从类型签名中推断Clifford代数等级并推导几何积稀疏性；以及一种自适应领域模型架构，通过正向模式协效应分析与精确正数累加在训练过程中保持这两个不变量。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统一化在Solomonoff通用先验的可计算限制下计算最大后验假设，从而使该框架的类型推理与通用归纳法处于相同的形式基础。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、跨层和跨推理请求叠加的开销。该框架通过构造消除了这一开销。