Ideas

[o0101]

Hash mining defines a function $F: I \to M$

where $I$ is the domain of input bits ${0,1}^i$ and $M$ is the mine target ${0,1}^m$.

So it's a permutation on ${0, \ldots, 2^{m-1}}$ (if injective/surjective).

This permutation could be used similarly to residue sets modulo some prime created with a generator. There seem to be many applications.

Aside from that, consider:

• Allow an option where the "mine" doesn't have to be a prefix but can appear at any sequence in the hash, at some offset in ${0, \ldots, w-1}$ (where $w$ is the digest byte width).

• Try "mining compression," where we search for an increment, seed, and offset that generate a target pattern, and declare success if encoding increment nonce, seed, and offset is shorter than the target pattern.

  This would generally have a high time cost for compression but fast decompression. It would be interesting to experiment with whether this could work at all, and to explore its asymptotic information representation quality (i.e., what entropy it approaches—perhaps something theoretical or akin to LZ).