Representational Consistency for Machine Learning Systems

We present a categorical framework for verifying that machine learning systems respect ---the requirement that inputs differing only by specified transformations receive consistent outputs. This is a framework: it verifies whether a system's behavior coheres with its specification, not whether that specification captures the right values. The framework addresses , one component of the broader AI alignment problem, and does not claim to solve value alignment, goal stability, or other alignment challenges. The mathematical foundation is and , which capture path composition and coherence laws without requiring smoothness or manifold structure. We define two types of morphisms: (changing representation while preserving meaning) and (changing context). Their interaction determines consistency properties. We define three : the _ measuring order-sensitivity of re-descriptions, the measuring context-dependence of transforms, and the _3 measuring higher-order composition sensitivity. These combine into the (Bd), a human-calibrated dimensionless metric with a five-tier deployment rating scale. A key result is the : every coherence defect splits uniquely into a part (eliminable by better canonicalization) and an (requiring specification changes). This separation distinguishes implementation bugs from specification contradictions. When re-description transforms form a Lie group acting smoothly, the framework recovers classical gauge theory as a smooth limit; we state this correspondence as a conjecture with supporting evidence. We address specification grounding via stakeholder deliberation, demonstrate on an autonomous vehicle case study, and provide computational complexity analysis. The framework makes the Bond Index---a measurable, auditable, actionable metric---the primary engineering deliverable for deployment decisions about representational consistency. Author preprint deposited for archival and citation. Draft — pending author review.