Generative AI systems were originally developed for exploratory contexts in which outputs function as suggestions, drafts, or hypotheses. In such environments — the space of thought — probabilistic language generation supports reasoning and creative exploration, and errors typically have limited consequences. Increasingly, however, these systems are deployed in operational environments where outputs serve as inputs for real-world decisions. In this operational space, statements must satisfy verifiable conditions before they can be relied upon. This paper argues that many governance challenges associated with generative AI arise from the deployment of systems optimized for the space of thought within operational domains. A central design assumption of many generative systems is that every query should produce an answer. While computationally efficient, this interaction model shifts the burden of validating uncertain outputs into organizational processes. The resulting activities — interpretation, verification, correction, escalation, and documentation — generate governance work that extends beyond the computational process itself. The paper introduces a distinction between bounded computational costs and potentially unbounded governance costs. Systems that are required to always produce answers can convert bounded infrastructure costs into expanding organizational governance obligations. Architectural mechanisms such as decision boundaries and non-decision states offer an alternative approach. By preventing the generation of outputs that do not satisfy operational validity conditions, such mechanisms transform governance from a reactive organizational activity into a bounded property of system design. The analysis suggests that the long-term economic viability of generative AI in responsibility-critical domains will depend less on model performance than on the architectural integration of mechanisms that constrain when and how operational statements are produced.