The is the assumption, not the reality.
Catalyst only reduces the energy required for the chemical reaction to produce hydrogen and oxygen from water. It does not reverse or eliminate the need for input energy. The system is still a net loss, or rather electricity is converted to heat in the process.
TANSTAAFL
—The system is still a net loss, or rather electricity is converted to heat in the process.—
My assumption was that for this to be viable, whatever burns the hydrogen and Oxygen, effectively re-uniting them into water, would power a generator to supply the electricity for the chemical reaction, and it would need to require less energy to produce the electricity than the amount of energy produced by the combustion of the hydrogen and oxygen.
IOW, for this to matter, it requires water and electricity to be applied to the catalyst. The result would be hydrogen and oxygen. The two would then be burned, as gasoline and oxygen are burned in an internal combustion engine. The power would be sufficient to turn a driveshaft, powering a vehicle, lawn mower, hydrolic pump or other tool, as well as a generator that produces at least as much electricity as it took to enable the splitting of the water molecule in the first place.
Otherwise I assume it would be pretty useless, taking in more power than it produces.