> looks like two arbitrary integers, but each one is a real decision with hardware consequences: block size determines how a block's resources are packed into an SM's fixed budgets, and grid size determines how evenly the total work spreads across the GPU's SMs. Picking both well is mostly a matter of a few rules of thumb plus one API that does the hardware-limit arithmetic for you.
The Register File and Occupancy derives occupancy as a fixed calculation against three hardware limits — registers, shared memory, and block/thread slots — and works a full example through all three. This page is the tuning counterpart: given that calculation, which levers actually move it, what raising occupancy buys in practice, and — just as important — where it stops buying anything at all.
Occupancy is defined in the glossary as the ratio of resident warps to the maximum an SM supports, and Latency, Throughput, and Latency Hiding explains why that ratio matters — resident warps are what supply the concurrent memory requests Little's Law demands. This page is about the other half: occupancy is not a tunable dial, it's the output of a fixed calculation against fixed hardware limits, and the register file is usually the tightest of those limits.