Originally I allowed the LLM to decide whether a subthread inherits the parent context, but had to back out of that one. I found quite expensively that if the parent context includes an instruction to do a task in a subthread, it could fly off into an infinite recursion of subthreads all burning tokens to delegate the task to a subthread!

So I've just made it so they don't inherit! If we find a situation where inheriting is useful and safe, it'd be easy to add again.