How about Pistorius style blades that extend your feet? There's no external power source[1] so would that be okay in your book?
[1]: *Assuming they're not "primed" by compressing them prior to the race starting so you bounce off the starter.
See my reply parallel to yours: how about we write that "book" and then we can all check together whether or not it's "okay" in that book. In contrast to a chronic case of never-ending what-aboutism.
But to answer your question directly: carbon blades would be consistent with what I've written in this thread.
Also see: flippers.
I think it'd be an interesting thing to study. When I was young and running a lot, I could beat (recreational) cyclists uphill, but they would smoke me on downhills. So there might be the kernel of a fun study there.
I guess my hypothesis is that, given equally fit bikers and runners, there's an incline where they will climb at equal speeds. Furthermore, at steep inclines, the runners will be faster and at shallower inclines, the bikers will be faster.
Doesn't seem too unlikely (or interesting, actually), given the weight of the bicycle. But the general shape of the curves might be interesting.