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：机器学习领域普遍假设模型正确性必须在事后强制执行。我们观察到，决定人工智能模型是否数值稳定、计算正确或与物理领域一致的属性并不必然需要事后约束——这些属性可在训练开始前的设计阶段完成验证，且仅需边际计算成本，尤其适用于部署在高风险决策支持与科学约束场景中的模型。此类属性共享特定的代数结构：可表达为有限生成阿贝尔群 $\mathbb{Z}^n$ 上的约束条件，其中推理过程在多项式时间内可判定，且主要类型唯一。基于此观察构建的框架整合了三个先前成果（arXiv:2603.16437, arXiv:2603.17627, arXiv:2603.18104）：一种携带任意标注作为持久余数据的维度类型系统，贯穿模型精化过程；一种程序超图，可通过类型签名单独推断克利福德代数阶数并推导几何积稀疏性；以及一种自适应领域模型架构，通过前向模式余效应分析与精确正数累加维持训练过程中的不变量。我们认为该组合产生了一个新颖的信息论结果：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约束下计算最大后验假设，使框架的类型推理与通用归纳处于同一形式基础。我们比较了四种当代人工智能可靠性方法，表明每种方法都会产生跨部署、跨层级、跨推理请求的复合开销，而本框架通过构造性设计消除了该开销。