When a forming planet's magma ocean interacts with its primordial atmosphere, chemical reactions should enrich the envelope with water vapor. The hydrogen is abundant, the temperature is right, the mixing happens continuously. But computational models reveal a hard limit: water production stops not when the hydrogen runs out, but when the magma exhausts its reactive oxygen budget. The atmosphere gets only as water-rich as the underlying magma can chemically support, and that limit is reached long before the protoplanetary disk disperses.
This is a cross-phase constraint. The composition of one system component—the gaseous envelope—is capped by the chemical inventory of an entirely different component—the molten rock beneath it. The atmosphere can't pull from an infinite reservoir; it's limited by what the solid planet can contribute. For sub-Neptunes, this means their observed water-rich envelopes can't form through magma-atmosphere interaction alone. You need late volatile delivery—comets, planetesimal impacts, something that adds material after the magma ocean freezes.
The oxygen exhaustion limit establishes a ceiling that no amount of mixing or equilibration can overcome. You can stir faster, heat longer, extend the interaction time indefinitely—none of it matters once the magma's oxygen is gone. The bottleneck isn't kinetic; it's stoichiometric.
This pattern recurs wherever material crosses phase boundaries or organizational levels. Soil nutrients cap plant biomass regardless of sunlight. Trace elements limit metabolic pathways despite abundant macronutrients. Institutional capacity constrains policy outcomes no matter how much funding arrives. The limit isn't in the thing you're trying to grow; it's in the substrate that has to supply it. And no amount of optimization within one phase can overcome depletion in another.