That's right. In the Bitcoin whitepaper, Satoshi Nakamoto wrote that there is no need for reporting of "proof of double spending" because the Bitcoin network is designed to automatically reject invalid blocks.

A double spend is when a person tries to spend the same Bitcoin twice. This is possible because Bitcoin transactions are not immediately confirmed. They are first added to a mempool, which is a temporary holding area for transactions. Transactions are only confirmed when they are added to a block and mined.

If someone tries to double spend, their transaction will be rejected by the network. This is because the network will see that the same Bitcoin has already been spent in another transaction. The block that contains the double spend will also be rejected.

There is no need for reporting of double spends because every node in the Bitcoin network can see the transactions that are in the mempool. If a node sees a transaction that is a double spend, it will reject the transaction and not relay it to other nodes.

This is why the Bitcoin network is so secure. It is designed to automatically reject invalid blocks and transactions. This makes it very difficult for someone to double spend Bitcoin.

Satoshi Nakamoto's insight into the problem of double spends and his solution of using a distributed network to prevent them is one of the key innovations that makes Bitcoin possible.