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Follow-up to: Parallel-resistant proof-of-work scheme?

Is there a proof-of-work scheme that:

  • can only be solved serially;
  • given the solution, can be verified in minimal time;
  • deterministically constructs the problem from some input, where the difficulty varies randomly dependent upon the input;
  • can be verified by any third-party.

I've looked into Time-lock puzzles and timed-release crypto (1996) [Rivest & Wagner] and Time-Lock Puzzles in the Random Oracle Model (2011) [Mahmoody, Moran & Vadhan], but I don't believe Rivest (1996) satisfies points 3 and 4, and I don't believe Mahmoody (2011) satisfies point 3.

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