Transformer-based large language models have become a prominent focus of machine learning. We develop adaptive domain models to supply domain-specific predictions and checks within language-model pipelines, as well as to serve direct machine automation efficiently. Their predictions can inform generation, while declared constraints and error bounds support checks on the calculations underlying proposed responses and actions. These feedforward and feedback paths aim to reduce domain errors while supporting use cases such as constraint solving for machine processes as well as preserving accuracy in a language model's conversational setting. Physical dimensions and geometric support restrict admissible computation, while a probability model expresses uncertainty. Our type and program hypergraph work connects these relationships to numerical and deployment obligations. We derive a natural-gradient calculation over forward tangent directions using a declared program metric, with a calibration example and a bound separating metric, derivative and solve errors. Forward differentiation and posit accumulation expose complementary resource and error tradeoffs. Our worked linear-Gaussian update connects posterior computation to error and a distribution-shift decision. Recent results from Urschel bound elimination growth probabilistically under distinct Gaussian-input and random-preconditioning hypotheses. Our unique approach to warm rotation binds candidate parameters to their numerical evidence and destination while each request observes a coherent model and state. We propose Bayesian distillation as a source of prior information. Our architecture offers a route to domain computations with explicit guarantees that can guide automated decisions and model responses. We specify experiments to evaluate prediction quality, domain errors across conversational turns, and total resource cost.

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