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I'll explain the steps I want to figure out.

I have an empty bitcoin core wallet.

  1. I backup the wallet and go offline.

  2. Someone sends bitcoin to this wallet and I can see it in balance.

  3. I restore my bitcoin core wallet to the initial point.

What will happen then?

I assume that I'll start over with the blockchain from scratch and what will happen is that initially the balance will be 0 (since my node is not yet aware of the transaction). So I'll need to synchronize up to the block where the transaction was included (this will take some time). At that time the balance will be updated. After that the synchronization will continue until its up-to-date with the head.

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Step 1. I backup the wallet and go offline.

Step 2. Someone send me a bitcoin to this wallet and i can see it(in balance).

When you're off the internet the wallet software will not know the transaction occurred until it is synced with other nodes on the network (P2P protocol). However, as long as the sender is online, the transaction will still be pushed into the mempool and eventually exist on the network (once included in a block) and you will be able to spend the output (so long that the transaction has been created properly).

Step 3 .Ill restore my bitcoin core wallet to the initial point..

If you've backed up your wallet file, you are essentially saving your private keys which is the only piece allowing you to spend TX outputs. If you reset your node or import your wallet into a computer that is not yet fully synced, the balance will remain 0 up until the block containing your transaction.

I assume that ill start over with the blockchain from scratch, And what will happen is that initially the balance will be 0 (since my node is not yet aware of the transaction). So ill need to synchronize up to the block where the transaction was included (this will take some time). At that time the balance will be updated. After that the synchronization will continue until it's up-to-date with the head.

Yep this is correct.

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Step 1. I backup the wallet and go offline.

To be more secure you should create a wallet with an offline computer.

In general I'm confused how you use wallet and node. The wallet aims to be a private key, which is computed with a random input, the seed. The node is a program running, connecting to other programs of its art (p2p). This program gets information from the other programs and verifies on its own, if the information satisfies a given set of rules.

I assume that ill start over with the blockchain from scratch

So your assumption depends on the deletion/backup of the information you mentioned. If you deleted the wallet directory your node won't sync from scratch.

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