> 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-loss-column-the-linear-route.md).

# The loss column: the linear route

Handed the linear loop unchanged, the program the comparators run as their default benchmark, zkFOL proves fib(10,000) mod 7919 in 1.19 s at roughly 205 MB, against 40.67 s and 2.30 GB (RISC Zero succinct) and 50.39 s and 17.07 GB (SP1 compressed). The loss is real and stated: on the linear route zkFOL's verification time grows with the number of steps, 34.1 ms here, while the comparators' verification stays constant. The compiler's doubling rewrite is the default route precisely because it removes that growth; the same exact-integer claim by the default route is the 9.98 ms row in the first table. \[S, benchmark record]