Building equality trials require the cell buildings to be upgraded, not the weapons on the right. Every time you land on a cell it gains 1 level (2 levels when first trial unlocked, 3 when second etc). The 70 and 140 trials, though, take a lot of time and rolls.
 "Tabletop idle RE"){kind=icon}
 "Asteroid wars"){kind=icon}
you need to defend and upgrade your asteroids first