The Boolean Pythagorean Triples problem asks the following question:

Is it possible to partition the positive integers into two sets such that no set contains a Pythagorean triple (three numbers a, b and c with a^2 + b^2 = c^2)?

In 2016, Marijn J.H. Heule proved via computer search that the integers up to 7824 can be partitioned this way, but it is impossible to partition the integers up to 7825, thus resolving this as NO.

The first part can be trivially demonstrated by listing the partition, but there is no easy way to show the absence of a partition for the numbers up to 7825. The proof consisted of a summary of the steps taken by the exhaustive computer search, and thus was over 200tb in size, dubbed "the largest proof in the world" at the time.

Obviously, a brute-force computer proof like this is not satisfying. Will a concise, human readable proof for this problem be published by the end of 2025? It doesn't have to specifically be limited to 7825. If someone finds a simple proof that the integers up to 10^10^10 can't be partitioned, that would still count.