The problem here is leaks. Burning and recapturing is a carbon positive process without separately trying to recapture carbon out of the rest of the air. The

The problem here is leaks. Burning and recapturing is a carbon positive process without separately trying to recapture carbon out of the rest of the air. The air at large has a very low concentration of CO2, so the capture is unfavourable. Your apparatus is only going to touch so many CO2 particles to recapture them, asides from CO2 being energetically favourable And, once you have sequestered them, the sequestration also has to worry about leaks. If you're using a synthetic fuel, those leaks move you from -100% net release towards 0% net release. If you're using newly mined fuel, the leaks move you from 0% release towards 100% release This doesn't account for the energy requirements to create the fuel