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Agricultural artificial intelligence is increasingly shaped by a precision paradigm that treats good farming as the increasingly fine-grained optimization of inputs, outputs, risks, and operational decisions. This paradigm is attractive because it promises measurable efficiency, predictive control, and scalable decision support across complex farming systems. In climate-sensitive agriculture, however, the same orientation can narrow what counts as a good decision. The problem is that climate-sensitive farming is not merely a technical setting in which better data automatically produce better outcomes. Farmers must act under uncertainty, ecological variability, long time horizons, and ethically contested trade-offs involving productivity, resilience, livelihoods, and environmental stewardship. These conditions expose the limits of optimization as a sufficient guide for responsible agricultural AI. This article develops a conceptual framework that shifts the guiding principle of agricultural AI from precision to prudence. Prudence is understood as practical wisdom: the capacity to deliberate well about what is fitting, responsible, and contextually appropriate when action is necessary but certainty is unavailable. The framework therefore reorients AI from prescribing optimal decisions to supporting wise and accountable judgment. The article is based on a conceptual synthesis peer-reviewed publications across agricultural ethics, responsible innovation, precision agriculture, AI governance, climate adaptation, and science and technology studies. It critiques precision agriculture as an optimization paradigm, articulates prudence as a responsible AI principle, and develops a framework for climate-sensitive decision support. Two tables contrast the precision and prudence paradigms and present the proposed conceptual framework. The central argument is not that agricultural AI should abandon data, modelling, prediction, or decision support. Rather, responsible AI for climate-sensitive farming should use these capacities to enlarge human judgment rather than replace it. A prudent AI system helps farmers deliberate under uncertainty, compare trade-offs, question recommendations, and remain accountable for decisions that are ecological, social, and moral as well as technical.