From the root Merkle tree, it is shown that the exchange currently has BTC582,485.9302 BTC in its on-chain reserve while BTC575,742.4228 BTC belongs to customers of the exchange.
ok, they hold 0.5M of users BTC, but how do I know that this include mine bitcoins? How do I know if their liability is not 10x bigger (5M bitcoins) and this POR (proof of reserve) is not only a 10% fractional reserve?
because your balance is part of the account which totals the same as the blockchain holding
EG - i really simplifying it down to most basics to show how merkles can be used
imagine 2 pages of excel
page one is all the coins on blockchain held by a service. which totals 575k btc
and page 2 is customer balances which total 575m
where your name (hashed for privacy) is on page 2.
where other users are not revealed due to hashes to others knowing real names .. but they too can find their own reference hash in that page 2 list
EG
page 1 page 2
deposits user accounts(not in order)
1legacyuserA 10btc da42dab49777512b8f425b43a493816c -4btc
1legacyuserB 4btc 01880749a3a55a34659994ef23dcf0c3 -10btc
1legacyuserC 15btc 9db3b3f7b608880d0a7d19a5cc611fb8 -11btc
1legacyuserD 11btc e8836d7e6bcf77e6e9454b5c1f6ebbdf -15btc
then take the first 2 da42+0188. hash them
=95f309a30aac743c459b24afe8c9e51f -14btc
then take the second 2 9db3+e88. hash them
=d0569e38584ec9ff272270ebf9b37d7d -26btc
then take those two 95f3+d056 hash them
39cc18deff1270d8436687dc5a458e54 -40btc
total 40btc in custody
imagine you are first depositor userA of page1
and are the 0188 prefix hash of page 2
for demo i MD5 "Tytanowy Janusz - 10btc"
and for instance MD5 "userC - 15btc" is the 9db3 prefix hash
you can see your allotment hash is part of a accounting process which totals the same as page 1 total
as long as a users allotment is in that total the user is seen as being counted/included. thus "safe"
ofcourse its not 100% proof because a exchange can simply one day shout "we been hacked" and take all coins. but atleast being seen and counted is a better standing than having no count not included in any count