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I wonder if it will ever be possible for games like Super Mario Bros. to be "solved" in the sense that there is a formal proof of the shortest possible completion time (for a given category / ruleset of speedrun).
Presumably that would first require a disassembly of the game, with a proven compilation process back to the original ROM (something like what CompCert does[0]) and then, after enumerating all the possible glitches, building some sort of state machine that defines how the character can progress through each level.
[0] https://compcert.org/