The Eden Treaty is a promise to put an end to hatred, so to speak. It's a pact to cease the long-standing rivalry between Trinity and Gehenna. In other words, it's an effort to build trust in the place of hatred that would only continue to fester if left alone. You can think of it as a peace treaty between Gehenna and Trinity. However, now that the General Student Council president has gone missing, the pact is worthless. Eden is the name of the paradise from ancient scriptures. It's beyond me why the General Student Council president chose it to begin with. Perhaps it was because she had a sick sense of humor.
Are you aware of Kivotos' seven koans? The fifth one relates to paradise. "Can we prove anyone has ever reached paradise?" Like each of the koans, this question's intent is vague but it can be interpreted as referring to the inherent paradox in proving the existence of paradise. If paradise exists then the ones who reach it will remain there for eternity, forever enveloped in joy and satisfaction. If someone does elave paradise, it's because they weren't fully satisfied, so it was never a paradise for them. Therefore, those who reach paradise cannot be found--and should not exist--outside of paradise. So, can you prove the truth of someone who does not exist? The purpose of this fifth koan is to be nigh unanswerable. Does truth that cannot be proven become worthless? What is the true question masked behind such cynicism? Eden is the Paradise from scripture. It exists nowhere and cannot be found. In other words, it's nothing but a sweet illusion conjured by dreamers. You see? Surely, this is the metaphor behind the treaty's name.
Sensei. You may find the story that's about to unfold to be unpalatable. It's a story meant to make you uncomfortable, uneasy, and leave you unhappy. A cynical story that will make you doubt people and truth. Gloomy, sad, painful, and ultimately bitter. But entirely truthful. I ask that you not look away and see it through to the end. For that is your responsibility.