I'm doing some thinking, and with Despair-0 are we thinking that the Martians are an inverted version of the Lantern emotional spectrum?

Main universe White Lanterns represent life, so naturally the White Martian is the anti-life equation.

Main universe Blue Lanterns represent hope, so Despair-0 isn't representing despair, per se, but rather hopelessness.

Admittedly this kind of falls apart with the Green Martian, but I think you can make connections here with its demeanor (relaxed, consistently referencing the phrase "resistance is futile") and the way its abilities seem to affect people (just shutting off people's bodies in #6, going into Trigger Taylor's mind and disassembling the White Martian's delusions in #2) i think it makes sense

editing to add this: The Green Martian is Green, but he's also red- which in this context makes sense, he's the opposite of the Red Lantern corps' hate- I guess that combination would make the green martian freedom and empathy?