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The third explosion limit of hydrogen oxidation in closed vessels has always been thought to be the result of the competition between homogeneous gas-phase reactions and diffusion of hydroperoxyl radicals to the walls, where they are destroyed. It has recently been observed that this species actually follows a chemical-kinetic steady state in this regime, with the consequence that its diffusive rate toward the catalytic walls becomes irrelevant. Here we show that the critical explosion conditions are determined instead by the fate of hydrogen peroxide, which emerges as the controlling reactant for the resulting gas-phase chemistry. A simple, accurate analytic expression for the third explosion limit follows from identification of the critical conditions for existence of weakly reactive, diffusion&-reaction solutions, thereby providing the answer to a long-standing problem that in early work was characterized as being hopelessly difficult.