There is no set time for a cycle to complete, or in your definition, take 4ppm of ammonia and convert it to nitrates in 24 hours. There are many factors that go into that equation, surface area of rocks, state of the rocks when water was put in the tank, flow through the rocks.. which all that equates to proper living environments for bacteria to colonize on. You use a proper amount of good clean cycled live rock out of a running tank and toss in a bottle of Tim's on top of that, your looking at 24 hours tops for the tank to be cycled and ready for fish, use clean dead/dry rock, your looking at 5-7 days, you use good live rock and shrimp method, 7-14 days, and if you use dead rock and the shrimp method, your looking at 3-4 weeks for the same thing on average. With so many unknown variables there isn't a way anyone can say how long any tank will take to cycle to your definition.
i know... i wasn't saying there was a set time limit... that's just when i believe a tank is cycled.