Oops, you’re right about the typo i will correct that now, i do appreciate this pointing out cause most of our beginners can get confused with this most especially when the topic is dealing with understanding what is actually recorded on the blockchain.

And on the proof of reserves point, users should understand also that seeing an exchange controlled address holding a huge amount of Bitcoin doesn’t prove by itself that every customer balance are fully backed. Exchange still have to show how this Onchain  holdings relate to its liabilities to customers.

So useful information can be given to users with proof of reserves, but also it shouldn’t be treated as same as having direct ownership of the coins.

The part worth internalizing: on-chain you can watch the exchange reserves move, but you can never verify your claim against them without the exchange cooperating. Proof-of-reserves tries to patch this with a Merkle proof that your balance is included in their liability set, but it cannot prove control of the withdrawal path and says nothing about off-chain liabilities. So the honest statement is: an exchange balance is an unsecured claim on a private database, enforceable only by the operator solvency and goodwill. The withdrawal is the only moment custody actually changes hands. Everything before it is accounting.

That logic extends past storage to how coins get moved between chains. I am on the team building HadesDex, a no-KYC swap interface, and the design rule we work to is exactly the question this thread asks: at any point do the coins sit in an address the user does not control. Our answer is wallet-to-wallet, the interface never takes custody at any step of the route. Whether it is us or any other service, that is the right question to ask before you send: if funds ever rest in an address you do not hold keys for, it is an exchange balance with extra steps.

In the past, I didn't really understand this, but I made it simple by using the same matrix as they do in banks and digital cash applications.

You see money as a number in those industries. Either in your cellphone or in your computer. But it remains a number until you cash it out. Real cash. That real money that is in circulation unlike what you see in your digital cash application. It can be the same way in Bitcoin.
You put in exchange or a trading website it becomes a number only that is visible to your eye. But once you withdraw it and put it in your hard wallet, that becomes real Bitcoin. It's not just a number anymore, it's Bitcoin.
I think for those who are having trouble understanding this, we must simplify it by using what we experience now in the financial industry.

Everything on exchange are numbers, it's like their data place manage in their servers. It's when you requested for withdrawal they send money to you, everything remain inside their wallets and they are a automated. They control both hot wallet and cold wallet, but the hit wallet is the busiest of them all, in each blockchain they have coins in there that is why it's dangerous to keep money in exchanges, if anything happen to their wallet, there will be no person to save everyone that have coins there.

I do use exchanges to buy, sell and swap but I have peace of mind more when my coins are off exchanges. The way Mexc was freezing users wallet some days ago makes me rethink the decision. I do have some Bitcoin left anytime I sell some part of my Bitcoin but it made me change completely. They look cool for use until they suspect you of anything, they wouldn't think twice before they block your account.