I don't understand what are you trying to prove. Apple shares represent the ownership of something (multinational technology company). Fiat currencies also represent the ownership of something(debt certificates). Bitcoin is a system for digit manipulation, and as such it has nothing to do with ownership, i.e. by owning the result of digit manipulation you own nothing.
lol
firstly i have apple shares. but i would never say i am the CEO of apple. .. as you say its a "representation"
firstly i have some fiat.. but i would never say i own debt.. as you say its a "representation"
secondly with shares, Apple can dilute the shares even without their "representative" owners consent
secondly with FIAT, banks can inflate the currency even without their "representative" owners consent
but bitcoin is different. it cant simply just change the rules without its owners consent
bitcoins blockchain actually is so transparent you can follow every transaction back to its mined block reward. you cant do "digital manipulation" in bitcoin.
i have a many bitcoin hoarded. but lets just say i have bitcoin address that i play with daily and i can guarantee you that you will not be able to stop me doing things with my coins. you cant:
freeze my funds
destroy my funds
take ownership of my funds behind my back
dilute my coins
inflate my coins
counterfeit my coins
destroy the transparent trail back to its source
destroy the relay effect that allows spending
the coins i own i own. not by representation. but by actual ownership.
now with that said..
as long as bitcoin has a purpose/utility. then it has value.
and bitcoin does have purpose/utility.
so i do own bitcoin which has value. which means i do own something.