Doom doesn't even have a (variable) random seed, it's deterministic like an NES game and has built-in record/playback that's just a frame by frame list of player moves.
…hang on, this is starting to feel like Elliptic Curve cryptography: it’s trivial to prove a demo file is a “solution” to a random-seeded Doom map, but nontrivial to work-backwards to generate a demo-recording.
The heart of Bitcoin is just "Find me a number between 0xf80000 and 0xff0000 whose SHA-1 hash starts with eight zeroes..."