Earlier quoted context omitted.
This is not true. Modern cryptography is not breakable via brute force any more, nor will it ever be. You can prove that the amount of energy required assuming a thermodynamically ideal computer is more than will ever be available in our galaxy, with classical computing. Breaks of symmetric crypto or hashes that are practical require an actual cryptographic weakness, whose existence is not a given. Then there's quant…
That is not true. There is nothing provable about hash functions. The best that you can say is that there is no known algorithm that can calculate a pre-image for any given hash function in less than some super linear time. You certainly cannot prove that no such algorithm exists. If you can prove it please publish a paper you will be revolutionize mathematics.
If your algorithm is not linear in the size of the key/hash space, it's not a brute force algorithm. It's a cryptographic break.
There is no proof that such algorithm does not exist, nor is there any proof that it does. Therefore you can't claim it definitely does. That's my point.