But they can't see who else is or is not accounted for within that total. If an exchange publishes proof of reserves of 10,000 BTC, and no customer has more than 10 BTC, then they will all be falsely reassured. But turns out the exchange is hiding the fact they have 100,000 customers all with 1 BTC and are massively fractional reserve.
ok lets delve into this more
ok binance has ~26m customers and a publicly viewable address list of reserve totalling ~575k btc
lets call it an average of 0.02211538 a user
what you are trying to say is that "what we dont know" is that they might have PoR of only 57k reserves. and only 1000 customers listed in the merkle with ~57btc average, which doesnt tally to the true customer holdings..
sorry but no.. just no
each person can see they are part of the merkle. and the merkle totals up to the same amount as the reserves
the merkel hash of a users leaf is their account details and balance hashed.. and outside the hash is a clear text of the balance aswell
users can check the balance(clear) matches their balance thats hashed to confirm nothing shoddy happening with their leaf(no miscount of their balance)
then for the clear text balance they can see all balances add up to the total. and that total matches the known bitcoin reserve addresses total
knowing they are included in the total. meaning knowing the reserve owner has enough coins to meet all of those clear text balances, no matter who they are. it shows they are included and not forgotten
there is no "negative " balance as that will be easy to spot
.
if you want to go opposite and say "imagine if CZ made an account and put 10k coin and added that to the merkle
then the clear text balances would total 585k coins instead of 575k coins.
which as long as the new 585k coins match the public bitcoin address reserves of 585k coins. then it simply means there are enough coins in binance control at that time to not only pay all users that can be seen and self verify they are part of the merkle total. but cz too
.
problems only arise when the merkle total does not tally with the reserves total. .. and thats the point. showing they do tally shows .. wait for it.. proof of reserves
if people have a hash. but cant find their hash in the merkle.. that too is a problem because then CZ is not tallying all users meaning there are more users balances not accounted for compared to the reserves addresses.
but if every user is found in the merkle. then it tallies
...
now with all that said
even with things tallying up
there is not much to stop a business from just one day moving funds out. disabling account access running off to an island and shouting "i been hacked" while sipping a cocktail on a beach holding all reserves to himself, while pressing a bankruptcy announcement button on his phone with an evil laugh