This article develops an interactional model of corrigible artificial intelligence without attributing a self, conscience, remorse, or moral interiority to the system. Large language models can apologize, hedge, revise, cite, refuse, and self-critique, yet these behaviors may remain fluent continuation unless correction has a binding pathway. The article proposes answerability architecture as a design and governance layer for corrigible AI interaction, organized in three nested levels. First, core answerability uses contact gates to test claim status, evidence, uncertainty, falsifiers, correction warrant, burden, risk, trace, and escalation so that warranted correction can change what happens next. Second, the agentic extension moves the unit of corrigibility from isolated answers to trajectories involving authorization, reversibility, memory, handoffs, execution, monitoring, and repair. Third, future-system implications extend the same requirement to goals, generated subgoals, progress proxies, bounded autonomy, verification capacity, corrective independence, and legitimate stopping. The model distinguishes prompted corrigibility, where users ask a model to be more careful, from architectural corrigibility, where correction is distributed across system instructions, verification tools, interface design, evaluation, human workflow, and institutional responsibility. It also requires selective revision: warranted correction should bind, unsupported correction should be resisted, and unclear correction should trigger verification. The central claim is simple: AI does not need a self to be made more correctable. It needs architectures in which evidence, uncertainty, consequence, and accountable human judgment can change what happens next.