I also discovered that C can go as low as 1.05 if we also allow 1.05 sqrt(N) stored items, with 3 kangaroos alone, and only addition group operations. And still people believe BSGS would work faster. for whatever reason, with TB of RAM.. I let them continue believing that.
Can you provide a link?
I only have experimental proofs (e.g "it works as advertised"). Don't ask why though. I'm not a number theorist. It's basically the 3 kangaroo method combined with the van Oorschot parallelization method, without using DPs.