switches

The count follows from three inputs and one topology rule, and getting it wrong by the leaf-to-spine half is the classic error. The arithmetic, the radix check that says two tiers is enough, and the power the transceivers add that nobody put in the budget.

Wire GPU number three of every node to the same switch and the collective that matters most never leaves it. The rank mapping that makes the layout pay, the switch and cable count for a thousand GPUs worked out, and what happens to a job whose ranks are assigned in the wrong order.