I surely don't have any evidence, but are financial systems obeying mathematics and natural laws, or not? If yes, there might be self-similarity to be found at different scales of price action. It's a fascinating topic to investigate, but have yet to find anything tangible to use in trading other than dumb default values as placeholder for order of magnitude (ie. using multiples of 1.618 instead of 2 or 10). The Phi-family of numbers, all purely derivable from phi, is the only "number" existing that is perfectly self-similar and self-symmetric in so many ways as it is, so anyways merit wonder and appreciation. Anyways, if one finds something, it'll be in the probabilistic domain, and not certainty.
Fib numbers are just cognitive reference numbers. It's a result of human bias.
It might be better to build a system with integers like 1.0000 in USDCHF, 1.25000 in EURUSD, 1.50000 in GBPUSD, which often form resistance levels and prices often reverse once they cross these points but that rarely happens but this is a result of human bias too.