> For the complete documentation index, see [llms.txt](https://docs.moduluszk.io/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.moduluszk.io/performance-the-prover-envelope/the-floor-a-bounds-check.md).

# The floor: a bounds check

Prove that a committed value lies in a range, with nothing to compute. This is the price of a proof at all. The comparator columns are unchanged from the fib table because the work never left each machine's floor; RISC Zero charges the same 32,768 cycles here as it does for the doubling run. zkFOL: 1.53 ms prove, 0.54 ms verify, roughly 3 MB. Ratios: 2,420x to 32,200x on prove, 100x to 5,700x on memory. \[S, benchmark record]