Not to be insane, but I just realized the possible Biblical reference to Caleb's arm.
"And if your right hand causes you to sin, cut it off and throw it away. For it is better that you lose one of your members than that your whole body go into hell." (Matthew 5:30)
In most if not all of Caleb's memories, the first hand he touches you with is his right. He resonates with you in Yearly Nostalgia with his right hand, he hesitates to touch her with his right hand. The apple in Exclusive Aftertaste is held in his right hand while it's in mc's left. In Wayward Wonderland, it's his right hand that takes mc's when he makes his vow, it's his right arm that holds her as they leave the fluctuation. Even in Clearwind Glide, the hand he uses to guide mc to fly is his right. Painful Signal is the entire focus of the loss of his right hand (arm). That, because he severed that sin, he can't even feel you anymore.
Caleb did this knowingly- purposefully. And why did he do it? To protect you. He minimized the damage of the explosion (perhaps his Judgement Day...?) to ensure that you wouldn't suffer the ramifications of his own sin, he severs the source. In that moment, he makes the decision that who he was will die. He rids himself of his sin, his connection and love, because he resigns himself to the truth that it would be better to lose his sin rather than lose himself entirely and burn in damnation. Because even if he's lost a part of himself, he still exists to do one thing. And that is to protect you. In life, in "death", and everything in between.