Gwern: I think you understand this, but for the benefit of other readers:
The strategy of enumerate, run in parallel, and pick the first to halt doesn’t give Kolmogorov complexity. It gives an upper bound. There might be some shorter program that will halt and give the appropriate output, but it just hasn’t gotten there yet when you find the first thing that halts.
Gwern: I think you understand this, but for the benefit of other readers:
The strategy of enumerate, run in parallel, and pick the first to halt doesn’t give Kolmogorov complexity. It gives an upper bound. There might be some shorter program that will halt and give the appropriate output, but it just hasn’t gotten there yet when you find the first thing that halts.