If 100% of the money is evenly distributed to every citizen, there is not a cent left to fund any corruption. Ideally the minimal administrative costs should not even come out of the carbon tax, of which fully one hundred percent should be evenly distributed to every citizen.

Presumably there would be some wrangling about how to measure CO2 emissions in certain harder to objectively measure contexts, but they're still not getting any of the money, they might just sneak in a way to not pay their full share. And we know with low variance how much CO2 is emitted by a unit of motor fuel or natural gas or coal, which represent the bulk of emissions.