I know Ethereum is a POW blockchain where forks take place. The transaction event is issued after executing the transaction on the node. If a fork occurs, is there a possibility that the transaction will not be included in the main chain? How do you verify that the dapp is completely in the chain when that event occurs?

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Proof of Work is all about probabilities. In theory you can never be 100% certain that a certain block will stay in the canonical chain (the main chain) - there is always a (small) chance that a history block will be reorganized and all subsequent blocks as well.

Basically you just have to decide on an acceptable threshold. The more blocks that were mined on top of the block you are interested in (the one with your transaction) the more certain it is that the block will stay in the canonical chain. Centralized exchanges call this number the "number of confirmations". So they may require, for example, 6 confirmations before a transaction is accepted.

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