Here's some criticism because I think this is neat! And well put-together! But you need to make clear which effects happen at each level. Players can - and should - check it. But you're making content and want it to be as good as possible, so should do it for them.
Sense Arcana - Cool effect! First, flip the magical effect and the monster orders. It makes more sense (based on the name and feel of the whole build) to list them the other way around. Furthermore, it makes more sense to put the short one first. I'd also remove the full cover issue.
Arcane Ward and Warding Hand are listed as titles, but refer incorrectly to each other. I like the effect overall! It's unique and balanced and feels cool. You definitely need to rewrite it though, it took a lot of parsing on my part to figure out what you were saying.
Nova is fine.
Censor is fine.
Aura of Protection - we're too close to Paladin's now. Make it something different.
Aura of Discovery is awesome!
Improved Arcane Nova - see Aura of Protection.
Insulating touch is nice.
Academies!
Discovery:
Thirst shouldn't include perception.
Rapid Ritual is great.
Illusions is good.
Decentralization is a little too niche. Maybe give it an additional effect.
Enlightenment is amazing. I love it.
Protection!
Ward - I think, and this probably comes down to taste, that this should be temporary hit points. This isn't a cleric class.
Arcanist's wall is amazing.
Rapid Shielding - consider including an 'errata' style note that DM's may rule not to have it work with other halving effects - evasion, etc.
Bulwark - now this is a cool effect.
Barrier - the wording here doesn't follow how temporary hitpoints in 5e. It's also insanely strong. If I go 20 Con at this level I have, on average, 214.5HP. This puts me with 419? Maybe a little much.
Nullification!
Zone is too powerful this early in the game. This fucks a lot of DMs up and is probably un-fun.
Scar, aura, mind, entity are all great.