Self-host Voxtral Small on dedicated GPU clusters

Alan Turing proved the halting problem is undecidable using a contradiction argument. Assume there exists a program, H, that can examine any program and input and correctly decide whether that program will eventually halt or run forever. Turing then constructs a new program, D, that uses H as a subroutine. Program D takes a program as input and does the opposite of what H predicts. If H says the program halts, D enters an infinite loop. If H says it runs forever, D halts. Now consider running D on its own code as input. If H predicts that D halts, D will loop forever. If H predicts it loops forever, D halts. In both cases, H is wrong, which contradicts the assumption that H always works. works. Therefore, no general algorithm can decide whether arbitrary programs halt.