The logical difference between the longest chain and the heaviest chain lies in whether they support Nash's non-cooperative game. Longest chain: A Turing ordinal logical system that evolves in the direction of block height as a hyperfinite iterative direction. It diverges to infinity and cannot converge to a unique invariance. Heaviest chain: Adds an ordinal logical system based on Nash's game theory, using the game of work difficulty to make the Turing ordinal logical system converge to a unique state. The gap between the longest chain and the heaviest chain: It’s missing a PoW model of Nash's non-cooperative game.