fleet sizing

A 400B dense model on 10 trillion tokens is 2.4 × 10²⁵ FLOPs, 43 days of pure compute on 16,384 H100s, and about 380 interruptions along the way. The order in which to derive every number, the layout and the data rate, the checkpoint and failure budgets, and the schedule that survives its own arithmetic.

The fleet equation solved for GPU count: about 6,200 H100s at 40% MFU, why it rounds up to a power of two, and the reasons a good answer adds 15% before naming a number.

Two constraints per replica, memory and throughput, each derived from the model and the traffic; whichever binds sets the users per replica, and the replica count follows with headroom. The full chain from 1,000 users to a number of nodes.

6ND to a compute budget, the fleet equation to a GPU count, the rental rate to a bill: 64 H100s, about 19 days, roughly $75k plus a buffer. The chain, the reasons the answer is 64 and not 59, and the memory check that says the fleet is compute-sized, not memory-sized.