Every institutional argument for AI as a climate tool follows the same rhetorical move: acknowledge the energy cost, then pivot to the efficiency dividend. Fortune's piece [10] and NVIDIA's Earth Day post [9] both perform this pivot. The Reuters Sustainable Switch report even documented the problem — AI's water and energy consumption — within a genre that structurally demands a solution turn. What none of these pieces supply is the arithmetic that would confirm the ratio: that optimization gains exceed consumption growth over any specified timeline. They assert equivalence…