For reference:
All artifacts have "At the beginning of your upkeep, sacrifice this artifact unless you pay 1 Mana."
At the beginning of the upkeep, the Kataki-granted abilities will all be placed on the stack, but won't resolve yet. Then he can tap Welder to put its ability on the stack targetting Mox Ruby and Black Lotus. While the Welder's ability is on the stack, he taps Mox Ruby for mana, then allows the ability to resolve. Ruby is sacrificed, Lotus is put into play, and then the Kataki-granted abilities will resolve one by one. Ruby is already gone, so he doesn't pay for that, and he uses the mana from the Ruby to pay for the Sphere of Resistance, and Mountain for the Juggernaut (or vice versa). Black Lotus wasn't in play at the beginning of the upkeep, so its Kataki-granted ability doesn't trigger.
