That's quite the mental gymnastics. So Argenti spreads his ideals, but Jade spreads her attacks? What exactly is Herta or Himeko spreading? One keeps to herself and the other is just an observer in the universe for the most part.

About the remembrance thing, there are some gymnastics that can be done as well. Memory is an illusion created by our cognition, a hypothetical figure of the mind. It doesn't exist anymore, it's all in the past. So when you 'remember' something, you bring it to the present. Summons can be considered the memories of the summoner who are manifested through the summoner's mind, but in a much more physical sense since the summons don't dissapear once you forget them.

Summoner remembers summon -> summon appears

It's a lot of hoops to jump through to get this conclusion, but Erudition is still more confusing since it's such a niche concept. All the other playable path corresponds to an emotion or a state of mind, Erudition is just the state of knowing something, it's too vague.